The Norwegian came under immense pressure at the club following the 5-0 defeat to Liverpool in Manchester towards the end of October before picking up two positive results against Tottenham Hotspur and Atalanta BC in the Premier League and Champions League respectively.
There were sections of the home support that appeared to boo Solskjaer during the match, but the club's former striker is not fearful that he could be sacked as head coach.
"No I don't [think he is on borrowed time]. I have good communication with the club all the time which is up front and honest. I work for Man United, I want the best for Man United. As long as I am here I want to improve this," Solskjaer told reporters.
Man United, who could be 11 points off the top of the Premier League table entering the November international break, will be back in action away to Watford on November 20.