The Frenchman has been benched for United's last two league games and did not play a single minute in the Red Devils' 4-1 victory over Fulham on Saturday.
Tuttosport reports that Pogba's old club closely monitor his situation as the 25-year-old midfielder remains at odds with Mourinho.
Their Sunday front page headline read: "Pogba immediately!".
The Italian paper says the Frenchman's relationship with the Portuguese coach could be beyond repair and that a January move would satisfy all sides involved.
The win over Fulham, United's biggest this season, was Pogba's second straight match started on the bench as he only came on the pitch with 15 minutes to go against Arsenal on Wednesday.
After beating the Cottagers, Mourinho warned Pogba he had to "play with the same mentality as the team" to regain his position.
The Portuguese coach had also stripped the Frenchman off vice-captaincy earlier this season after he criticised his manager's tactics.
Mourinho, however, said yesterday Pogba would start the Champions League clash against Valencia on Wednesday as United are already through to the round of 16 but fight with Juventus for top spot in group H.
The Frenchman moved to Juventus in 2012 having snubbed a contract extension at Old Trafford.
He won four Serie A titles with the Italian giants and featured in the 2015 Champions League final, but rejoined United in 2016 following his record-breaking £89million transfer.
Pogba was also France's key player in their World Cup triumph last summer.
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