The Portuguese midfielder has rejected two contract offers from United, with his current agreement due to expire at the end of the season. The club, however, hold an option to extend his stay by a further 12 months.
Manchester United are keen to keep their captain, but Fernandes is understood to want to assess the direction of the club under Pochettino before making a decision about a new deal.
A source told The Sun: “Bruno wants to see what happens for the rest of this season before committing.
“His relationship with the club has been up and down in the last few years.
“He enjoyed a best-ever season but is unhappy with some of the decisions since Sir Jim Ratcliffe and Ineos bought into the club.
“He knows Poch is a good manager but wants to see the club back him properly — he and some other players think they have been set up to fail this season.”
The same source claimed there was frustration among players over the club's recruitment and decision-making, particularly the failure to bring in another left-back during the summer.
“The players believe the failure to buy another left-back in the summer was inexcusable.
“They are bemused by some of the decisions.
“There is a disconnect between the players and the hierarchy.”
Fernandes has been a central figure at Old Trafford since joining from Sporting in 2020, but United's difficult season has created uncertainty around his future.
He was recently dropped by Michael Carrick following the defeat by Como in the Champions League, having reportedly criticised the manager's tactics. Carrick was subsequently dismissed after United's poor start to the Premier League campaign.
Pochettino has now been appointed as his successor, and United will hope the Argentine can help persuade Fernandes to remain at the club.
The midfielder's contractual position gives the club some protection. If a new agreement is not reached, United can activate the additional year before January, preventing him from negotiating a pre-contract agreement with an overseas club during the winter window.
That option is important because, without an extension, Fernandes would be able to speak to clubs outside England from January with a view to leaving on a free transfer when his contract expires.
United have made clear they want him to stay, and the club are expected to continue discussions with his representatives. Fernandes, though, has already turned down two proposals, meaning the arrival of a new manager may be an important factor in determining whether negotiations progress.
Pochettino's first task will be to improve results and restore confidence at Old Trafford. Whether he can also convince the captain that United are moving in the right direction could prove just as significant for the club's longer-term plans.