Solskjaer signed a three-year contract upon taking permanent charge in March 2019 and has since led United to the top of the Premier League table, with a genuine title challenge possible.
The United manager's long-term future had come under scrutiny following the 6-1 defeat to Tottenham in October and last month's Champions League group stage exit, but the Old Trafford hierarchy have always kept faith.
Solskjaer said on Tuesday that there had been no discussions on extending his stay at United beyond the next 18 months but thanked his superiors for standing by him during difficult moments.
"We haven't had any discussions yet," he said. "For me, I just keep on doing my job as well as I can.
"I've said it many a time we looked at the squad, looked at situation we were in, we put a longer term plan in place.
"We knew there would be some patchy periods and that we would have to stay strong mentally.
"The leadership they have shown has been very strong and steady and I'm very grateful for the communication that has been open and honest all of the time."
Solskjaer also expressed his sympathy for Frank Lampard, who was sacked by Chelsea on Monday after losing six of his last nine Premier League games.
"One thing I know for sure is Frank doesn't want any of us to feel sorry for him," he said. "I know his character and mentality and I’m sure he'll bounce back and have a very good managerial career.
"He went through a patchy spell, a short spell, not long ago they were top of the league, it’s the first dip of form they really had under Frank so I’m a little bit surprised but it's not my job to comment on what's happened at Chelsea.
"I just comment on our club and we knew we were going to have some rough and patchy periods and they stood strong.
"I’ve had good backing from the club and the leadership has been very steady which I have been very grateful for because we have been through two or three bad spells of form of course.
"But we don't know what's happening behind the scenes, you probably don't know either what’s happening behind the scenes here either and it's not for me to keep talking about our communication but it's always sad when someone loses their job."