You can declare a dependency property in the converter class, declare your converter as static resource and bind the property to a view model property.
This will work:  
<Window x:Class="..."
        x:Name="_this" 
        ...>
<Window.Resources>
    <local:DepPropConverter x:Key="Convert"
        MyList="{Binding DataContext.YourListInViewmodel, Source={x:Reference _this}}"/>
</Window.Resources>
<CheckBox IsChecked="{Binding item, Converter={StaticResource Converter}}"></CheckBox>
The converter:      
public class DepPropConverter : DependencyObject, IValueConverter
{
    public static readonly DependencyProperty MyListProperty =
        DependencyProperty.Register(
            nameof(MyList), typeof(IList), typeof(DepPropConverter));
    public IList MyList
    {
        get { return (IList)GetValue(MyListProperty); }
        set { SetValue(MyListProperty, value); }
    }
    public object Convert(
        object value, Type targetType, object parameter, CultureInfo culture)
    {
        //your logic here
        return value;
    }
    public object ConvertBack(
        object value, Type targetTypes, object parameter, CultureInfo culture)
    {
        //your logic here
        return value;
    }
}