The Scotland midfielder currently finds himself trapped in the relegation zone at the East Anglian club with their remaining two matches of the domestic season coming against title contenders Chelsea and an Arsenal side still endeavouring to secure Champions League football for next term.
Snodgrass' raw ambition means that relegation to the Sky Bet Championship would force him to review his options with a year of his contract remaining, and he is perfectly open about the fact that the top division in England is the only place he has ever wanted to play.
However, he has been a Celtic supporter since childhood and has dropped the strongest hint yet that he would be willing to talk, in the right circumstances, should they opt to turn consistent, long-term interest into a water-tight proposal.
"I was in Scottish football and there's always a part of me that is saying: 'You've a point to prove'," said the former Livingston player.
"I played here as a kid, but I'm a different specimen now and I do everything I can to be a top professional. I live and breathe football.
"Everything I've driven towards is in the Premier League. That's a big pull for me. I come up here on international duty and speak about different things with the lads. I want to be successful and Celtic are a very successful club.
"They win things. They could've won the treble this year and winning things appeals to me, but the Premier League is where it's at and I'd be lying if I said anything other than that.
"There are two sides of the coin, really. 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 possible level.
"If options come in the summer, I'll look at them. It's testament to me that a club that Celtic are linked with me. They are a fantastic club and they've reached the last 16 of the Champions League a couple of times in the past few years.
"I've watched them since I was a kid and I'm flattered, but everything I do is geared towards keeping Norwich City in the Premier League."
Snodgrass believes Norwich can still upset the odds to avoid relegation and insists he would seek to fulfil his contractual obligations there should they achieve their mission improbable. "What division we're in will be relevant," he stated. "If things go according to plan and we stay in the Premier League, I'll have a year left and I'll honour that every way I can.
"As a player, though, you want to play at the highest possible level and that's why I'm giving everything I can to keep Norwich up. This club gave me my chance. It's a fantastic club and I've loved every second there."
Of course, the current Celtic manager, Neil Lennon, is of interest to Norwich as they scour the market for a new, long-term head coach and Snodgrass has no qualms in recommending life at the Norfolk club to the Northern Irishman.
"If he did get the Norwich job, he'd be coming into a fantastic club with a great support and great people about the place," said Snodgrass.
"I'll let the powers-that-be decide who gets the job, though. Whatever decision Neil has to make, he'll make himself, but he's done a fantastic job at Celtic and good luck to him in his future."
Snodgrass will certainly require some kind of rub of the green if he is, indeed, to guide Norwich away from the relegation trapdoor. The odds are stacked against them and he realises exactly what will be required to keep his team afloat.
"We should have more points, but the league doesn't lie," he said.
"It's going to take blood, sweat and tears to try and get any points against Chelsea and Arsenal because both of them are fighting for something. It's a big ask, but we'll give it our best shot."