Here is an example with several notes :
1- you don't need to extend JFrame, use a custom JPanel and set it as the content of the frame.
2- override paintComponent and not paint, paintComponent has the single responsibility of painting the current component (your panel).
3- use a Shape object (here an Ellipse2D.Double), because it has a lovely contains(int x,int y) method .
4- add a MouseMotionListener to the panel and check when the mouse is moved, if its location is inside your shape.
5- Display the frame in the Event Dispatch Thread
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.event.MouseEvent;
import java.awt.event.MouseMotionAdapter;
import java.awt.geom.Ellipse2D;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.SwingUtilities;
// see note 1
public class CirclePanel extends JPanel {
    // see note 3
    Ellipse2D circle = new Ellipse2D.Double(0, 0, 100, 100);
    public CirclePanel() {
        // see note 4
        addMouseMotionListener(new MouseMotionAdapter() {
            @Override
            public void mouseMoved(final MouseEvent e) {
                if (circle.contains(e.getX(), e.getY())) {
                    System.out.println("Mouse entered");
                }
            }
        });
    }
    // see note 2
    @Override
    protected void paintComponent(final Graphics g) {
        super.paintComponent(g);
        Graphics2D g2d = (Graphics2D) g;
        g2d.setColor(Color.BLACK);
        g2d.draw(circle);
    }
    public static void main(final String args[]) {
        // see note 5
        SwingUtilities.invokeLater(new Runnable() {
            @Override
            public void run() {
                JFrame frame = new JFrame();
                CirclePanel t = new CirclePanel();
                frame.getContentPane().add(t);
                frame.setTitle("Tutorial");
                frame.setSize(150, 150);
                frame.setVisible(true);
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            }
        });
    }
}