And Hull could have little say in the matter then, when Dawson will be free to talk to other clubs upon the expiry of his contract.
The 34-year-old was due back on Trentside as early as this weekend, however, with Hull Forest's visitors in the Championship.
But according to his manager, Nigel Adkins, Dawson is unlikely to recover from the injury which kept him out of Saturday's defeat at Preston North End.
Discussing his captain's future with the Hull Daily Mail, Adkins said: "I want Michael to be the captain and the leader, I didn’t want him to go on deadline day but things go on and it’s very frustrating.
"I made my stance perfectly clear I didn’t want Michael to go, he’s captain of the club and I want him to extend his stay here, that’s been my stance all the way through and that isn’t changing.
"Whatever the situation is Dawson is still a Hull City player, he has been struggling with a groin injury. He said it himself, I’m not blagging it, I’m serious.
"I’ve got a lot of time for Michael Dawson. We’re in a relegation battle and the last thing I want to do is lose the captain and the leader of our football club and that’s Michael Dawson. He’s very good at that and I have a lot of respect for him and the way he is and the way he has been for this club over the years.
"I can’t see him being fit next week against Nottingham Forest and we’ll have to see where we go from there. It’s in Michael’s interest to be fit and playing and it’s in our interest too."
Dawson spent eight years on Nottingham Forest's books before being sold to Tottenham Hotspur, alongside then teammate Andy Reid, in January 2005.
The former England international returned north to sign for Hull three-and-a-half years ago, and helped them to promotion via the Championship play-offs in 2016.