Mourinho denied any falling out with Pogba when confirming the decision, but Sky Sports' footage from training the following morning suggested all is not well.
Mourinho has been openly critical of his star midfielder in recent times, saying that his work rate isn't up to standard.
Mourinho said something which prompted a shocked reaction from Pogba and the heated conversation continued as they joined the group.
One source has said, however, that Mourinho is "picking fights with his players and then asking them to play for him", with another claiming the atmosphere between Mourinho and his squad has been hard since the players returned to preseason training in July.
Ryan Giggs says Liverpool have their strongest ever Premier League XI
The German will have been encouraged by Shaqiri's impact and may feel he can use him in Saturday's trip to Stamford Bridge. The Reds exited the League Cup on Wednesday night, as they suffered their first defeat at Anfield since January.
Paddy Power make it 1/3 that Mourinho departs Old Trafford first, while making it the same odds-on price that at least one of the duo will have left United by the start of next season.
The French World Cup victor was stripped of the club's vice captaincy on Tuesday, and a fresh report on Tuesday night from Mail Online claims that Mourinho made the decision following Pogba's admission.
'The only truth is that I made the decision for Paul not to be the second captain any more, ' said Mourinho.
Manchester United were beaten by Frank Lampard's Derby County at Old Trafford on Tuesday night in the EFL League Cup while Paul Pogba watched from the executive box. A club source claims the decision actually went down well with the players.
But while there is a sense of exasperation with Mourinho's approach, there is also an air of helplessness among the players due to the realisation that the club remains supportive of the manager. To come to Manchester United and not to just nick one, but I think to play the way we played, doing all the things we have been working towards in a short space of time.
But the midfielder has made several comments which some have considered to be veiled digs at Mourinho this season, the latest coming following the 1-1 draw with Wolves on Saturday, and the Portuguese confirmed reports of the change after the Derby clash.