Pogba has endued a mixed time at Manchester United since his £89m move from Juventus in 2016.
Reports over the summer claimed Juve would be open to re-signing the midfielder if United made his available.
No deal is currently in the pipeline and United’s board seem keen on keeping Pogba for the long term – even if his manager Jose Mourinho may see things differently.
Pogba is all set to play against his former club on Tuesday night when they clash in the Champions League at Old Trafford.
And Italian newspaper Tuttosport claim Allegri remains hopeful of soon signing the midfielder once again.
Tuttosport claim Juve director Fabio Paratici is working out how to snap up Pogba in the future.
According to the report, Allegri’s relationship with Pogba would be the driving force behind any deal.
The manager acted not only as a manager but ‘also a life teacher, a confidant’ during Pogba’s time in Italy.
It is a management style Paul Pogba does not get with his current coach Mourinho.
Whether Juve would ever act on their interest in Pogba remains to be seen.
The Turin club spent £105m on Cristiano Ronaldo’s arrival from Real Madrid in the summer – agreeing to pay the forward £106m over four years.
That deal could only be brokered with FIAT helping to sponsor the transfer.
Meanwhile, reports claim Real defender Marcelo wants to join Ronaldo in Turin.
Juve are said to be open to the transfer but would have to offload Alex Sandro – possibly onto Chelsea – in order to finance the deal.
Manchester United would likely not want to sell Pogba for anything less than £100m.