United host PSG at the Champions League last 16 on Tuesday and also Liverpool in the Premier League on 24 February.
The Norwegian has won 10 out of 11 matches since taking control in December.
“There are still a few months of the season to do anything I can for the club,” explained Solskjaer.
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Inspired by reporters if wins PSG and Liverpool – either side of an FA Cup fifth-round trip to Chelsea – will get him the occupation full time he added:”You’ve many ways [of requesting that question].
“You need to alter the script. That is too easy.”
United were first sixth in the Premier League, 1-1 points beyond the top , once Solskjaer succeeded Jose Mourinho on 19 December. Since that time the club have won nine out of 10 Premier League games to grow to fourth location.
They have also beaten Reading and Arsenal to set up the tie in Stamford Bridge on 18 February.
“I have loved every single minute of this ever since I walked in and met with the players,” the 45-year-old added.
“Moving to this match [using PSG] I don’t think we are in a better mindset with form and confidence so we’re really excited about the upcoming few matches coming up”
Solskjaer was appointed interim boss two weeks later seeing United paired with PSG in the Champions League draw of December – which he watched on TV with his own son.
He explained:”I had been watching it with Noah and we said,’Wow, that is a difficult challenge’. However, we’ve given the greatest possible opportunity to ourselves.
“I have found out what type of team we have, we’re looking just like a team, we’re agreeing about how we must approach matches.
“If there is a time to really go into big games such as this, it is now.”