However, it will depend on whether or not Norwich remain in the English Premiership.
If the Canaries are sucked into the relegation spots - they are currently just five points above third-bottom Fulham, who they play tomorrow, then have a horror run-in with games against Liverpool, Manchester United, Chelsea and Arsenal - the Hoops are ready to make their offer for Snodgrass.
But, if Norwich stay up, Celtic know the Scotland player will most likely still be priced out of their range.
The 26-year-old Glaswegian is understood to be prepared to take a big cut in wages to move is family back north.
Celtic's interest in him in the last transfer window fell flat because Norwich placed a price tag of £6million on the attacking midfielder they bought from Leeds for £4m in July, 2012.
That figure will be much harder to justify if the club is dropping down to the Championship, especially as Snodgrass - who signed a three-year deal when he moved to Carrow Road from Elland Road - will have only 12 months of his deal left to run and could sign a pre-contract agreement at the end of this year.
With manager Chris Hughton sacked and replaced until the end of the season by former Under-18s coach, Neil Adams, there is expected to be a lot of movement in and out of the club.
Snodgrass - who had an altercation with some Norwich fans during a game at Carrow Road in January - will attract a lot of interest.
He has scored six goals for the club in their troubled season. Only Gary Hooper, with seven, has found the net more.
But Celtic hold the trump card because of the pull of Glasgow to the player.
Snodgrass said in January: "It's my hometown and I stay five seconds away from the stadium. I'm a Celtic fan."
Neil Lennon is in England this week, taking in games as he checks on the form of targets already identified, and searching for other potential signings.
He has made a striker his priority.
But, with Georgios Samaras expected to move on when his contract runs out this summer, an experienced player who can drive in from wide areas and provide a goal threat is also on the Hoops' shopping list.
Snodgrass - who was brought up in the Gallowgate just along the road from Parkhead - fits the bill.
But while both the player and the Hoops are keen to do a deal, Norwich's fate as a Premiership club could hold the key to them becoming united.
Snodgrass was given the chance to train with Celtic as a kid.
But Livingston became his first club before he went on loan to Stirling Albion, then won a move to Leeds in 2008.
He became captain of the Elland Road club and got his first Scotland call-up while playing for them in League One in 2009.
Injury caused him to pull out of George Burley's squad, and it was two more years before Snodgrass made his debut for his country.
He has since won 15 caps and established himself as a regular under Gordon Strachan.