United have struggled this term under Solskjaer, and currently sit ninth in the Premier League table with just 35 points from 25 games.
They have lost more league games than they’ve won since Solskjaer became the permanent manager, and speculation over his future continues.
And Italian outlet Sport Mediaset believe the Red Devils could line Allegri up to replace the Norwegian at Old Trafford.
The Italian won the Serie A titles during his time in Italy as boss of Juve and AC Milan and is expected to return to management after a year off this summer.
Aside United, French champions Paris Saint-Germain have also been linked with the 52 year-old.
Their boss Thomas Tuchel hit the headlines for the wrong reasons in recent weeks, after clashing with star forward Kylian Mbappe.
The 2018 FIFA World Cup winner was substituted in their 5-0 Ligue 1 win over Montpellier earlier this month.
The German was also left unimpressed with the timing of Neymar’s 28th birthday party, which the whole squad attended at a Paris nightclub just 48 hours before a league match at Nantes.
Tuchel is under-pressure to lead PSG past the Champions League quarter-finals this season, with the French champions facing Tuchel’s old club, Borussia Dortmund, in the round of 16.
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