Snodgrass joined Norwich from Leeds United in the summer of 2012 and has a further season to run on his contract at Carrow Road.
He is currently battling to keep Norwich, who are in the relegation zone on goal difference, in the Premier League and he has suggested he will stay with the club, if they avoid the drop.
However, the Scotland international wants to play at the highest level and acknowledged that Celtic hold a place 'deep in my heart'.
"What division we're in will be relevant," the former Livingston youngster is quoted in the Daily Record. "If things go according to plan and we stay in the Premier League, I'll have a year left and I'll honour that.
"As a player, you want to play at the highest level and that's why I'm giving everything I can to keep Norwich up.
"Everything I do is geared towards keeping us in the Premier League as this club gave me my chance. It's a fantastic club and I've loved every second here.
"I'm flattered to be linked with Celtic as I've watched them since I was a kid. I was also in Scottish football and there's always a part of me that thinks I've a point to prove there.
"Celtic hold a place deep in my heart because I've watched them and they're the team I support, but it's all about being the best you can and playing at the highest level possible.
"The Premier League is where it's at and I'd be lying if I said anything other than that. But if other options come up in the summer, I'll look at them."
Celtic boss Neil Lennon, meanwhile, has been linked with the managerial job at Norwich, who currently have Neil Adams in charge following the recent sacking of Chris Hughton.
Regarding the rumours concerning Lennon, Snodgrass said: "There's a lot of speculation involving Neil Lennon.
"I don't know what he wants to do or if he wants to go on and test himself with a club down south. But if he did get the Norwich job he would be coming into a fantastic club with great supporters and great people about the place.
"Whatever decision Neil Lennon has to make he'll make it himself. But he's done a fantastic job at Celtic in the last few years and good luck to him in the future."