The Italian departed Juventus last summer after winning five consecutive Serie A titles and reaching two Champions League finals.
He was replaced by Maurizio Sarri in the Turin hotseat, and has remained out of work throughout the 2019/20 campaign.
According to the Mail Online, the reason for Allegri’s hesitation in accepting a new job is that he hopes to take over at Old Trafford.
Solskjaer’s side fell to a 3-1 defeat to rivals Manchester City in the Carabao Cup semi-final first leg at home on Tuesday, and the Norwegian described it as their worst performance of the season.
Allegri is believed to be very interested in the United job, and it is claimed that Arsenal were dissuaded from approaching the 52-year-old in December, when they were looking for a successor to sacked boss Unai Emery.
But Solskjaer has insisted he feels in no danger of the sack, despite failing to win any of his last three games in all competitions.
United’s next task is a home clash with Norwich City in the Premier League on Saturday.
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