Manchester United have sounded out former Tottenham manager Mauricio Pochettino as a potential replacement, according to the Manchester Evening News.
United have made a disappointing start to the season having finished the last term strongly and have lost their last two games - a Premier League fixture against Arsenal and a Champions League trip to Istanbul Basaksehir.
Should they lose to Everton on Saturday, United could end the weekend in 17th place in the domestic table.
When asked about whether he feared for his job after the loss in Turkey on Wednesday, Solskjaer insisted that he was not worried about his future.
"I decline to comment on such a thing. Of course, it's early on and opinions are out there all the time. You've got to stay strong," he told reporters.
"I'm employed by the club to do a job and I do that to the best of my ability with my staff."
Pochettino has been out of work since leaving Tottenham last November and should United move for him, they will not have to pay Spurs any compensation.
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