Reed won his first major championship at the weekend as he claimed the Green Jacket by finishing the Masters 15-under par.
Meanwhile, Woods had a mixed tournament as he struggled to shoot below par until the final round on Sunday.
The American has only returned from surgery on his lower-back injury this year but has showed glimpses of his old self.
And Reed wants to see his hero return to his best so that he can challenge him for major honours in the future.
“It is awesome to have Tiger back and to have him back playing well,” Reed told CBS.
“It is one thing to come back and ease into it and play Valspar and make the cut.
“We have seen some glimpses of the old Tiger coming back and he is playing some good golf.
“That is one of my dreams: I want Tiger to come back and play how he has played.
“I haven’t been able to experience it in life, I have only seen it on TV.
“I would love to see that.”
Reed fought off the challenge of Rickie Fowler, Jordan Spieth and Rory McIlroy to claim the win at Augusta.
He has now set his sights on achieving the world No 1 ranking.