Former midfielder Michael Carrick, who was on Solskjaer's coaching staff will be in temporary charge, starting with a trip to Spain for a Champions League match at Villarreal in the group stage on Monday.
The show of confidence in Solskjaer follows a second-place finish in the Premier League and a trip to Europa League final.
Solskjaer also seemed reluctant to trust his injury-depleted bench of substitutes, even when Villarreal brought on fresher players and started to take the initiative in extra time.
Cavani scored twice in each game while De Gea produced some fine saves as United advanced 8-5 on aggregate.
The France international was forced off near the end of the first half of United’s 3-3 draw against Everton in the Premier League on Saturday.
The last time United was top after 17 games of a league campaign, Alex Ferguson was in charge in what proved to be the final season of his long managerial tenure at Old Trafford.
If ever there was a signal of the team’s decline since the retirement of Alex Ferguson, it’s that United will be featuring in Europe’s oft-derided second-tier competition
Manchester United faced a 1-3 defeat in their opening game of the Premier League season to Crystal Palace on Saturday.
Solskjaer said United tried to prevent the 18-year-old Greenwood from joining up with England, believing he needed some rest after his breakthrough season.
Maguire was given a suspended 21-month sentence last month for assaulting a police officer, swearing, resisting arrest and attempted bribery during an incident on the Greek island of Mykonos in the offseason.
Manchester United were beaten 1-2 at the semi-final stage for a third time this season, this time Sevilla ending their run with a come-from-behind victory.
Dortmund sporting director Michael Zorc poured cold water on any potential deal on Monday by stating Sancho will be at Signal Iduna Park next season.
Manchester United secured a 1-0 win in extra time through a Bruno Fernandes penalty in the quarterfinal of the Europa League on Monday.
Martial scored his 23rd goal of the season against LASK in last week's Europa League last-16 victory.
Although named in a 30-man squad for the Europa League, Jones will be unavailable when Man United take on FC Copenhagen in the quarterfinal on Monday.
The two played at the 1998 World Cup when Norway reached the last 16 and beat Brazil along the way. The Norwegian team was bursting with talent then but hasn't qualified for a World Cup since.
On Thursday, Alexis Sanchez signed a three-year contract with Serie A side Inter Milan.
Manchester United confirmed their place in the top four with a 2-0 win over Leicester City on Sunday.
Former Manchester United captain Roy Keane believes that Frank Lampard has done a better job than Ole Gunnar Solskjaer in the 2019/20 season.
The Spaniard was guilty of letting two goals in on either side of half-time, one from Olivier Giroud and another from Mason Mount, as Chelsea thumped Manchester United 3-1 to secure a place in the final.
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