The Red Devils turned to their former striker Solskjaer as their interim manager after Manchester United parted company with Jose Mourinho in December.
Solskjaer was appointed as the club’s permanent boss at the end of March after Manchester United went on an incredible winning run under their club legend.
But the 20-time English champions ended the 2018-19 season with one victory in seven outings to finish the Premier League campaign on a disappointing note.
Solskjaer’s side have collected five points from their opening four games, including a 2-1 loss to Crystal Palace at Old Trafford last month.
Chelsea FC, on the other hand, appointed Lampard as Maurizio Sarri’s replacement in the summer.
Lampard’s side have also earned five points from their opening four fixtures, although the west London side are unbeaten in their last three outings.
Former Chelsea FC striker Sutton believes Lampard will survive the season at Chelsea FC but he has doubts about whether Solskjaer will still be Manchester United boss next summer.
“There is a willingness to show patience with Lampard,” Sutton told the Daily Mail.
“He is working in the post- Hazard era and putting up with a transfer embargo.
“Lampard should last the season, but I’m not so sure Solskjaer will.
“He took over at Old Trafford last season, finishing with one win in their last seven Premier League games. Now their troubles are continuing.”
Manchester United will welcome Leicester City to Old Trafford in their next Premier League game on Saturday 14 September, while Chelsea FC will make the trip to Wolves.
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