Everton have been linked with a man who Sam Allardyce knows well.
Allardyce managed Van Aanholt at Sunderland and then spent £14 million on taking him to Selhurst Park following his appointment at Crystal Palace 12 months ago.
And Burley believes that the former Chelsea youth could join up with his old manager for a third time.
He told ESPN: "Well I think this is something that could happen, primarily because Allardyce has worked with him at Crystal Palace, and only for that reason am I going to say that this could potentially happen.
"I've no idea if Allardyce will bring him in but he has worked with the player so that could happen."
Right-back Cuco Martina has been plugging gaps on the left-hand side of defence in recent weeks after Leighton Baines suffered a knee injury.
Even if Baines was fit, the Toffees probably still need an upgrade. He turns 33 next Monday and is less reliable for the Goodison Park club than he once was.
Whether or not Allardyce goes for Van Aanholt remains to be seen, but a left-back should be among the priorities in January.