Gascoigne has been in the thoughts of English football fans this week after being admitted to a treatment centre in Arizona for alcohol addiction.
Rooney trained with Gazza as a teenager at Everton and has admitted that the playmaker made a lasting impression on him during those early sessions.
He said: "It's a shame, of course (Gascoigne's current situation). He was a hero of mine growing up and it's sad for everyone to see and read about. My best wishes are with him and hopefully he can get himself out of this situation. I'm sure everyone, every England fan and every Paul Gascoigne fan wishes him the best of luck.
"I trained a couple of times at Everton with him. I was only about 14 or 15 but, of course, for Everton to sign a player of that stature was incredible. I was watching him play for England for years so to then have him going to the same place as I was going to train was great and to see some of the stuff he could do with the ball.
"I would dream of doing stuff the way he did, the way he ran with the ball. Probably the closest thing I've seen to Gazza is Jack Wilshere, where he gets the ball and runs at players a lot quicker and a lot stronger than people realise."
Rooney has scored 17 times for club and country this season despite being injured during the busy Christmas period.