Responding to reports linking him with a transfer to the Scottish Premier League giants, Rasmussen told Danish television station TV2: "A move to Celtic would obviously be interesting for me.
"As long as nothing is certain, it's difficult for me to say much.
"They're a big club and it has always been a dream of mine to play outside Denmark - but we will have to wait and see what happens."
Earlier on Friday, Hoops boss Tony Mowbray played his cards close to his chest regarding the 24-year-old, but would not deny that he was set to move for the player.
He said: "I don't want to sit and discuss any players because you move from one to the next to the next.
"So let's move on and we will wait and see."
St. Johnstone v Celtic Half Time Result: Draw 11/8