If you don't want the Drop list to show up like a popup. You can customize it this way just like me (it will show up as if on the same flat, see image below):

After expand:

Please follow the steps below:
First, create a dart file named drop_list_model.dart:
import 'package:flutter/material.dart';
class DropListModel {
  DropListModel(this.listOptionItems);
  final List<OptionItem> listOptionItems;
}
class OptionItem {
  final String id;
  final String title;
  OptionItem({@required this.id, @required this.title});
}
Next, create file file select_drop_list.dart:
import 'package:flutter/material.dart';
import 'package:time_keeping/model/drop_list_model.dart';
import 'package:time_keeping/widgets/src/core_internal.dart';
class SelectDropList extends StatefulWidget {
  final OptionItem itemSelected;
  final DropListModel dropListModel;
  final Function(OptionItem optionItem) onOptionSelected;
  SelectDropList(this.itemSelected, this.dropListModel, this.onOptionSelected);
  @override
  _SelectDropListState createState() => _SelectDropListState(itemSelected, dropListModel);
}
class _SelectDropListState extends State<SelectDropList> with SingleTickerProviderStateMixin {
  OptionItem optionItemSelected;
  final DropListModel dropListModel;
  AnimationController expandController;
  Animation<double> animation;
  bool isShow = false;
  _SelectDropListState(this.optionItemSelected, this.dropListModel);
  @override
  void initState() {
    super.initState();
    expandController = AnimationController(
        vsync: this,
        duration: Duration(milliseconds: 350)
    );
    animation = CurvedAnimation(
      parent: expandController,
      curve: Curves.fastOutSlowIn,
    );
    _runExpandCheck();
  }
  void _runExpandCheck() {
    if(isShow) {
      expandController.forward();
    } else {
      expandController.reverse();
    }
  }
  @override
  void dispose() {
    expandController.dispose();
    super.dispose();
  }
  @override
  Widget build(BuildContext context) {
    return Container(
      child: Column(
        children: <Widget>[
          Container(
            padding: const EdgeInsets.symmetric(
                horizontal: 15, vertical: 17),
            decoration: new BoxDecoration(
              borderRadius: BorderRadius.circular(20.0),
              color: Colors.white,
              boxShadow: [
                BoxShadow(
                    blurRadius: 10,
                    color: Colors.black26,
                    offset: Offset(0, 2))
              ],
            ),
            child: new Row(
              mainAxisSize: MainAxisSize.max,
              crossAxisAlignment: CrossAxisAlignment.center,
              children: <Widget>[
                Icon(Icons.card_travel, color: Color(0xFF307DF1),),
                SizedBox(width: 10,),
                Expanded(
                    child: GestureDetector(
                      onTap: () {
                        this.isShow = !this.isShow;
                        _runExpandCheck();
                        setState(() {
                        });
                      },
                      child: Text(optionItemSelected.title, style: TextStyle(
                          color: Color(0xFF307DF1),
                          fontSize: 16),),
                    )
                ),
                Align(
                  alignment: Alignment(1, 0),
                  child: Icon(
                    isShow ? Icons.arrow_drop_down : Icons.arrow_right,
                    color: Color(0xFF307DF1),
                    size: 15,
                  ),
                ),
              ],
            ),
          ),
          SizeTransition(
              axisAlignment: 1.0,
              sizeFactor: animation,
              child: Container(
                margin: const EdgeInsets.only(bottom: 10),
                  padding: const EdgeInsets.only(bottom: 10),
                  decoration: new BoxDecoration(
                    borderRadius: BorderRadius.only(bottomLeft: Radius.circular(20), bottomRight: Radius.circular(20)),
                    color: Colors.white,
                    boxShadow: [
                      BoxShadow(
                          blurRadius: 4,
                          color: Colors.black26,
                          offset: Offset(0, 4))
                    ],
                  ),
                  child: _buildDropListOptions(dropListModel.listOptionItems, context)
              )
          ),
//          Divider(color: Colors.grey.shade300, height: 1,)
        ],
      ),
    );
  }
  Column _buildDropListOptions(List<OptionItem> items, BuildContext context) {
    return Column(
      children: items.map((item) => _buildSubMenu(item, context)).toList(),
    );
  }
  Widget _buildSubMenu(OptionItem item, BuildContext context) {
    return Padding(
      padding: const EdgeInsets.only(left: 26.0, top: 5, bottom: 5),
      child: GestureDetector(
        child: Row(
          children: <Widget>[
            Expanded(
              flex: 1,
              child: Container(
                padding: const EdgeInsets.only(top: 20),
                decoration: BoxDecoration(
                  border: Border(top: BorderSide(color: Colors.grey[200], width: 1)),
                ),
                child: Text(item.title,
                    style: TextStyle(
                        color: Color(0xFF307DF1),
                        fontWeight: FontWeight.w400,
                        fontSize: 14),
                    maxLines: 3,
                    textAlign: TextAlign.start,
                    overflow: TextOverflow.ellipsis),
              ),
            ),
          ],
        ),
        onTap: () {
          this.optionItemSelected = item;
          isShow = false;
          expandController.reverse();
          widget.onOptionSelected(item);
        },
      ),
    );
  }
}
Initialize value:
DropListModel dropListModel = DropListModel([OptionItem(id: "1", title: "Option 1"), OptionItem(id: "2", title: "Option 2")]);
OptionItem optionItemSelected = OptionItem(id: null, title: "Chọn quyền truy cập");
Finally use it:
SelectDropList(
           this.optionItemSelected, 
           this.dropListModel, 
           (optionItem){
                 optionItemSelected = optionItem;
                    setState(() {
  
                    });
               },
            )