Asked if speculation about a permanent contract bothered him, the former United striker told reporters: "I love managing these boys and I love working here. I'm just doing the best I can every single day. If and when a decision is to be made, then we will see."
He said his deal with Molde had been terminated the instant he joined United, contradicting comments by his former employer.
Molde CEO Oystein Neerland said on Wednesday he expected Solskjaer to return after his stint with United ended, having signed last year to remain at the Norwegian club until 2021.
"That contract (with Molde) was terminated and I am contracted to United until the end of June," Solskjaer said ahead of Sunday's league trip to Arsenal.
"With the contract issue, you cannot have two contracts when you are a manager."
Solskjaer said defender Eric Bailly and forward Anthony Martial would be available for the clash at Emirates Stadium.
He hoped midfielders Nemanja Matic and Ander Herrera would also recover in time. "They just need to have another couple of days training with the team, they've done well in their recovery work."
Solskjaer also said he expected Marcus Rashford to kick on following the stoppage-time penalty that sealed a dramatic victory in Paris, comparing the young striker to the way Cristiano Ronaldo cut his teeth at Old Trafford before moving to Real Madrid in 2009.
"Rashy's goals sometimes are worldies and he does have a sensational strike of the ball," Solskjaer said.
"But you see the change in Cristiano's goals from when he was young to now, he scores more from inside the box and that's what Rashy has to improve as well."
(Reporting by Rohith Nair in Bengaluru; editing by John Stonestreet)
