Teenage full-back Putt has been troubled with a heel problem, while flanker Thompson had a groin injury.
The Plymouth-born pair could be back in contention for Albion’s match at Esher next weekend.
And their return could be timely with Royal Navy players Jarrad Hayler and Seti Raumakita set to go away on a training camp after today’s game with Coventry at Brickfields.
“Tom came back and did his first contact training session on Thursday and came through with flying colours,” said Albion’s director of rugby Graham Dawe.
“Unless he has an adverse reaction he should be available for next Saturday’s game at Esher.
“Cameron is also back in full training and, again, should be available next weekend.”
Putt, 18, proved himself one of National One’s top goal-kickers with a 74.19 per cent success ratio from more than 30 attempts.
He had also just scored his first try for the club when he got injured.
With Elliot Bale having recently returned from injury, Albion are not short of backs, but Dawe believes Putt will be determined to force his way back into the squad.
“He will certainly have to put in some good performances on the training field to earn his shirt back,” said Dawe. “But I would back him to give it a good go.”
Meanwhile, Albion forward Nile Dacres is hoping he can continue to be the club’s ever-present man.
Dacres is the only player to have featured in every single minute of Albion’s National One games this season.
Against Coventry today, he would clock up 1,500 consecutive minutes for the club, which is 25 hours of rugby.
“I have been quite lucky with injuries and luckily I have not picked up any cards either. Hopefully, that continues,” said Dacres, a summer signing from Moseley.
“But, as I’ve said before, I’m just going to take each game as it comes. However, I’m not going to complain about having too many minutes!”
Dacres is also Albion’s joint top try scorer with eight.
“I think me and Herbie (Stupple) are drawing on eight apiece at the moment, but it’s not like there’s a rivalry or anything like that going on!” said Dacres.
Albion have had 15 different try scorers so far this season. They have managed 53 tries in total from their 18 games, with 30 tries coming from backs, 21 from forwards and two from penalties.