Woods has been in erratic form since his return to golf after the allegations about his private life, finishing fourth in the Masters, missing the cut at Quail Hollow and tying for 19th at the Memorial last time out.
Fisher said: “This is probably the best chance we’ve got of beating him whilst he’s going through tough times in his life and a sticky patch in his game.
“So I’ve got to raise my game and I’d definitely take the challenge on if it were to come my way on Sunday afternoon playing with Tiger.”
Fisher added: “It would mean a great deal – I haven’t tasted a Major win yet but I know there’s one in there.
“I’ve come very, very close, I’ve put myself in contention a number of times but have not quite managed to walk through the door.”
The US Open begins on June 17.