After a hard start to the campaign, West Ham manager Manuel Pellegrini moved Rice into central midfield alongside Mark Noble and Pedro Obiang and the team's form experienced a turnaround.
Mourinho has come under intense scrutiny for the team's negative displays on the pitch and has faced questions over his position at Old Trafford, despite being the club's most successful manager since Sir Alex Ferguson left in 2013.
Football player's current contracts will expire in 2020.More news: Khmer Rouge Leaders Found Guilty Of Cambodia Massacre
The La Liga heavyweights are now sixth in the division and have failed to deal with the exit of Cristiano Ronaldo in the summer as they have only netted 20 goals in their opening 12 league matches and Solari feels Rashford can bring some much-needed youth into Real's ageing squad. Man United didn't back his attempt to sign a defender in the summer window.
The Gunners have been in scintillating form going forward this season but have struggled to keep the goals out at the other end, with reports claiming that Unai Emery will target a new centre-back in January.
However, Juventus are confident they would have the inside running on any deal and believe Pogba's strained relationship with Jose Mourinho could give them a chance of prising him away from the Premier League.
This story could gather pace in the coming weeks as the winter transfer window draws ever closer, with a huge bidding war for Rice looking like a distinct possibility.