Pogba – who said in June that “it could be a good time to have a new challenge somewhere else” – was absent for the International Champions Cup penalty shoot-out win over AC Milan in Cardiff with what Solskjaer had described as a “back spasm”.
It was reported on Friday night that staff and players were shocked when the France midfielder failed to turn up for the scheduled flight.
But Solskjaer said Pogba’s name being included in the party was down to an administrative error, and he was aware that the World Cup winner would not be travelling to Cardiff.
Asked whether he was concerned about Pogba’s commitment to United, Solskjaer replied: “I’ve no doubts at all.
“I wasn’t expecting him (on the plane). I spoke to him after training and he didn’t feel right.
“Paul will probably be back early next week training. It’s not an injury, he just felt some pain. We didn’t want to risk anything this weekend and he should be OK for Chelsea. I hope so.”
United, meanwhile, are close to completing the signing of Harry Maguire from Leicester.
The 26-year-old England defender will cost £80million – and Solskjaer expects him to be in contention to make his debut against Chelsea in next weekend’s Premier League opener.
“Hopefully the last little details will be in place, so we can announce something very soon,” Solskjaer said.
“Let’s get the last details over the line. But he’s played a few games over the summer so we’ll just have to assess him as and when.”
On his team selection for the Chelsea game, Solskjaer added: “I’ve got an idea.
“It’s been five good weeks, some players have done well to get into the team when you thought they would need some time.
“But eight days is a long time in football.”
Solskjaer also said he had spoken to Romelu Lukaku over a controversial social media post revealing confidential details of a training sprint session.
The Belgium striker, thought to be on the verge of a move to Serie A, took to Twitter on Friday to respond to criticism that he lacks pace by posting statistics from a running test on the Perth leg of United’s July pre-season tour.
Lukaku has since removed the post, which revealed he was second to only Diogo Dalot in a session, which charted the speeds of 22 other first-team players.
The tweet was accompanied by the words “lack of pace” alongside running emojis.
“I’ve spoken to Rom, that’s case closed,” said Solskjaer, who confirmed club captain Ashley Young will wear the armband when he is on the pitch.
Goalkeeper David De Gea skippered the side in Cardiff – a game United won 5-4 on penalties after Marcus Rashford and Jesse Lingard had scored in a 2-2 draw.
“David is in contention, but when Ash is on the pitch he will carry the armband,” Solskjaer said.