Click! program in Java Swing
Using an IDE, some changes are suggested automatically. For example:
Runnable and ActionListener can be replaced with Lambdas, 

        if(circle.contains(e.getPoint()))
            hover = true;
        else
            hover = false;


can be simplified to 

hover = circle.contains(e.getPoint());


Also, is it really intended that in Ellipse2D.Double(randomPositionY, randomPositionX, randomSize, randomSize) the first parameter is Y?

Usually if/else statements are used with braces.

In such small classes, the distinction between UI logic and business logic may not seem important, but as programs grow, it also gets more important. The Methods in your MouseListener seem to contain logic which could be extracted to a class or method. Although I am not a Swing expert, IIRC the repaint() method has to be called from the Event-dispatching thread, and could be therefore moved from generateRandom() into the Listener-methods where they are guaranteed to be called from the Event-dispatching thread.

The logic for generating a new circle could be refactored into an own class like this:

class CircleGenerator{
    public final static int MAX_SIZE = 100;
    public final static int MIN_SIZE = 10;
    private Random rand = new Random();

    public Ellipse2D.Double generateRandomCircle() {

        int randomSize = MIN_SIZE + (rand.nextInt(MAX_SIZE - MIN_SIZE) + 1);

        int randomPositionX = rand.nextInt(WIDTH - randomSize);
        int randomPositionY = rand.nextInt(HEIGHT - randomSize);
        return new Ellipse2D.Double(randomPositionX, randomPositionY, randomSize, randomSize);
    }
}