See attached screen shot.
I have made the 4 text box’s hyperlinkes to different reports.
Is it possible to have a some sort of formula which will say change the colour of the box when the cursor is hovered over the hyperlink like a webpage button could do?

Unfortunately SSRS does not allow events like
onHoveretc. The only thing you can do is to provide a label for the entry or to simply color the text using the properties section and set it to underline. However, this would mean at all times it would be underlined and colored.