The France international struggled to leave his mark on their Champions League clash on Tuesday night after Manchester United played out a 0-0 draw with La Liga side Valencia.
Pogba was particularly disappointing in the middle of the park alongside Marouane Fellaini and Nemanja Matic to plunge Manchester United into a deeper crisis.
The 25-year-old was stripped of the Manchester United vice captaincy last month after Pogba criticised the Red Devils’ tactics in a 1-1 draw with Wolverhampton Wanderers at Old Trafford.
Mourinho used Pogba sparingly in the second half of the 2017-18 season to fuel talk of a potential move to FC Barcelona but a deal ultimately failed to materialise.
Former Chelsea FC defender Burley believes Manchester United should consider selling Pogba given his poor performances since his club record move to Old Trafford.
“There is a lot of interest in Pogba,” Burley told BBC Radio 5 Live.
“He is close to being jettisoned. We are talking about getting rid of Mourinho. It would be quite to clever to cash in on Pogba as well. He hasn’t covered himself in glory either.”
Manchester United made Pogba the fourth signing of the 2016 summer transfer window following Mourinho’s appointment as Louis van Gaal’s replacement in May 2016.
Pogba played a significant role in Manchester United’s triumphs in the League Cup and the Europa League in his first season back at the 20-time English champions.
The France star was sold to Serie A side Juventus in an £800,000 deal from Manchester United in 2012 after Sir Alex Ferguson refused to guarnteee the midfielder a regular first-team sport.
Manchester United re-signed Pogba in a club record £89m deal from Juve in the 2016 summer transfer window after the France star won four Serie A titles in Juve
Pogba and his team-mates will be hoping to make amends for their winless run in the Premier League when Manchester United host Newcastle United on Saturday evening.
BIOGRAPHY: Learn more about Paul Pogba
The Red Devils have already lost to Brighton and Hove Albion, Tottemham Hotspur and West Ham United in the Premier League.
The 20-time English champions signed Shakhtar Donetsk midfielder Fred in the 2018 summer transfer window to help ease the creative workload on Pogba in the Manchester United team.
The Red Devils also recruited FC Porto defender Diogo Dalot and veteran England goalkeeper Lee Grant.
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