The former England international, 26, has rocketed up to the top of the list of expected Parkhead arrivals amid speculation that his contract with the Championship strugglers could be terminated this month.
The Sunderland Echo have reported that Celtic are keeping close tabs on Rodwell, who they previously tried to snap up on loan last summer.
Football Whispers, which gathers all transfer rumours across the globe and calculates the likelihood of them happening, rates it 3.0 out of 5 that Rodwell will join Celtic, with five the highest possible ranking and meaning it is a certainty.
The midfielder is ahead in the ratings of Leicester striker Ahmed Musa, who is rated at 2.9 to transfer to Parkhead, and FC Schalke striker Franco Di Santo, whose rating is 2.5.
Good move for Celtic?
Once billed as one of the outstanding talents in the English game, Rodwell has suffered a complete meltdown in form, fitness and confidence since swapping Everton for Manchester City in 2012. A move to Sunderland two years later has done little to arrest his decline and he has been limited to just two league appearances this season. Rodwell needs a change of surroundings and Paradise could be just the shot in the arm he needs. Should a pay-as-you-play contract be agreed, this could be worth a punt for Celtic.
This Is Futbol rating: 5/10
Likely to happen?
According to the Echo, Rodwell is on £70,000-a-week at Sunderland but there is no chance his next deal will be worth anywhere near the same. Should he negotiate a pay-off with the Black Cats, that will bring Celtic into the equation. The midfielder will need to take a massive pay cut and put his football before his wallet for a deal to be agreed.
This Is Futbol rating: 4/10