Solskjaer is under pressure after Sunday’s 5-0 defeat to Liverpool and another bad defeat this weekend could make his position untenable.
United co-chairman Joel Glazer, who will make the final decision, wants to give Solskjaer more time and is desperate for him to succeed.
But while United have delayed a decision to give themselves more time, Solskjaer has been given no guarantees he will remain in charge beyond the Spurs game.
It has been reported that Solskjaer has three games to save his job. United are away to Tottenham on Saturday and then travel to Atalanta in the Champions League next Tuesday before playing Manchester City at Old Trafford on Saturday week.
Solskjaer will be replaced if results continue to deteriorate before the international break next month.
Former Chelsea manager Antonio Conte, who has been out of work since leaving Inter Milan in the summer, would be interested in the job should Solskjaer leave.
Another potential candidate is former Real Madrid coach Zinedine Zidane, although he is said to prefer a move back to France to resume his managerial career.