The Manchester United interim manager has made a brilliant start to his spell in charge of the Old Trafford side following a return of 22 points from eight league games.
Their form under Solskjaer has put Manchester United in a position to challenge Arsenal and Chelsea FC for the final Champions League qualification spot.
In fact, the Red Devils can hoist themselves into the top four with a win against Fulham at Saturday lunchtime ahead of Sunday’s clash between Chelsea FC and Manchester City.
The 20-time English title winners will be eager to beat Fulham to warm up for the first leg of their Champions League last-16 clash against Paris Saint-Germain at Old Trafford on Tuesday.
Former Liverpool FC defeder Lawrenson believes Manchester United will beat Fulham to put them in a great position to secure a top-four spot.
“Manchester United are flying at the moment and it surely is only a matter of time before Solskjaer gets the manager’s job permanently,” Lawrenson told BBC Sport.
“I can only see one outcome here – another United win, which would be his 10th victory in 11 games as interim boss.
“That is a brilliant run, but I don’t agree with Manchester City manager Pep Guardiola that United are back in the title race. They are not in the running for that at all.”
Lawrenson added: “I worry for Fulham, who followed up their impressive 4-2 win over Brighton with a pretty limp defeat at Crystal Palace last weekend – when I thought they would dig in and get a draw.
“The Cottagers are now seven points adrift of safety and it seems like they cannot string two results together, which is a big problem for a team in their situation.
“I am not sure Fulham boss Claudio Ranieri has many cards left to play to try to change things around, and they are running out of games too.”
Manchester United have won nine of their 10 games under the Norwegian head coach after Solskjaer replaced Jose Mourinho in December.
The Red Devils have beaten both Arsenal and Tottenham Hotspur during their impressive run in the Premier League and the FA Cup.
Solskjaer has put himself in a strong position to get the job on a permanent basis.
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