The experienced stopper has been on the treatment table after picking up a back injury in the summer, but is now ready to push for a first-team place once again.
McGregor was forced to undergo an operation in July after it became clear rest would not solve the issue and it looks to have done the trick.
“Allan is back training with the first-team squad now and we’ll be looking to try and get him some match minutes with the Under-23s in the next couple of weeks before he progresses on to become available for first-team selection,” the Tigers’ head of medical services Rob Price explained on City’s website.
The news comes as another boost after it was revealed both Michael Dawson and Moses Odubajo are also closing on a return to the first-team squad.
Bournemouth are targeting Sheffield United's talented young Wales international David Brooks for a £10million summer transfer swoop.
Brighton midfielder Steve Sidwell has announced his retirement from the game.