After losing 3-1 to Liverpool on Sunday, United now find themselves 19 points behind their rivals after just 17 games of the Premier League season.
"They're nearly writing off this season and next season because if they appoint a new manager in the summer he's not going to have much time to look for new players".
Solskjaer had 11 years at United as a player, memorably scoring in the Champions League final against Bayern Munich to seal the treble in 1999, and spent a period as their reserve coach, working with the likes of Paul Pogba.
"Manchester United is in my heart and it's brilliant to be coming back in this role", Solskjaer said, per Man United's official website.
"We are confident they will unite the players and the fans as we head into the second half of the season", he added.
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Manchester United has found its replacement for Jose Mourinho, at least until the end of the season.
The appointment of Solskjaer to inject some life into United in some ways mirrors his playing career at the club where he scored 126 goals between 1996-2007, often as an impact sub. "We are happy to lend Ole Gunnar, we wish both him and the club success".
Mourinho was sacked on Tuesday with United having made their worst start to a league campaign after 17 games since the 1990-91 season.
In a statement released on Wednesday, MUST say the club needs to "put football expertise in charge of football decisions". I am looking forward to leading Manchester United until the summer.
Molde's season ended last month and does not resume until March 31, with Solskjaer unlikely to refuse the chance to manage such a prestigious club. "Meanwhile, I will closely monitor what is happening here at home (Molde)".
Now sixth in the Premier League table and 11 points adrift of the top four, he's got plenty of work to do.
Solskjaer is expected to speak to the media for the first time on Friday, with a frantic few days peaking on Saturday evening at Cardiff as his first match pits him against the only other Premier League club he has coached.
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