Sky Sports today reports there is no indication coming from the club that Solskjaer would lose his job.
As things stand, the 48-year-old is expected to be in charge when United face Watford after the international break.
Speculation was intense following the 5-0 humiliation by Liverpool, but Solskjaer survived despite strong links to Antonio Conte, who is now manager of Tottenham.
A United victory at Spurs together with a draw at Atalanta, which kept them top of their Champions League group last week, seemed to have calmed the situation.
However, the 2-0 loss to City reignited the questions over Solskjaer’s future.
Speaking following that City victory, former United defender Gary Neville suggested a decision would not be made until after Ed Woodward’s departure at the end of the year.
No decision has been announced as to a successor to Woodward, however, that process is not expected to have any bearing on decisions that may or may not be made regarding the manager, as ultimately the board makes such decisions as a whole with the final sign-off coming from Joel Glazer.