England manager Gareth Southgate (AFP)
Southgate's side host Albania at Wembley on Friday and travel to San Marino on Monday as they look to earn the four points required to qualify for next year's World Cup.
Chelsea midfielder Mount is recovering after a tooth infection kept him out of his club's starting line-up for their last three games and is unlikely to feature against the Albanians.
Manchester United left-back Shaw sustained a head injury in the derby defeat against Manchester City last weekend and is following concussion protocols.
The 26-year-old failed the head injury markers on the first day of his concussion absence, which has further delayed his potential return.
"I've got to check in with our medical staff for today's update. Obviously, the longer that goes, the less likely it is (that Mount and Shaw could be involved against San Marino)," Southgate told reporters on Thursday.
"It's different situations really. Mason's got to recover from this dental surgery.
"With Luke, there's very strict guidelines on concussion markers. I know, the early part of the week the first day he didn't pass the marker so that got shifted back and rightly, we're going to follow the guidelines on that but we might run out of time. We'll just have to see."
After a build-up period already marred by the withdrawals of Manchester United forward Marcus Rashford, Southampton midfielder James Ward-Prowse and West Ham midfielder Declan Rice, there was better news for Southgate about Grealish's availability.
"Jack's had some illness and has missed some training so, he's trained this morning with the rest of the group," Southgate said of the Manchester City forward.
"He's available for the game and he's ready if required."
- 'Never straightforward' -
Arsenal's in-form midfielder Emile Smith Rowe has benefitted from the rash of injuries as he received his first call-up to England's senior squad on Monday.
"Emile was close to being in the original squad when we announced it so we had no hesitation in moving him across," Southgate said.
"This is a group that makes new players and young players really welcome so I don't think it's a difficult environment to fit in.
"His quality has been apparent, in the way that he's trained so he's ready and we've enjoyed having him with us this week already."
England sit top of Group I, three points clear of second placed Poland, but they still have work to do in their last two qualifiers to ensure their World Cup berth.
All the fitness worries have made it a far from ideal preparation for Southgate, but he remains in confident mood, having urged his players not to repeat the mistakes of their draw at home to Hungary in October.
"Training's been very good. We've obviously had quite a few players withdrawing from the squad. But we're used to dealing with that," he said.
"It's never straightforward and we've just got on with it. I don't think anybody here would have felt there's anything unusual about the way that we've prepared.
"We have had a good focus this week on making sure we are on the front foot and pressing better than against Hungary."
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