The fan favourite joined on a deal until the end of the season 2018-19 season, after the sacking of Jose Mourinho in December.
The intention was for Solskjaer to return to his role at the Molde helm in May, with the Norwegian club’s chief executive Oystein Neerland saying they are happy to “lend” their manager to United.
Last week Neerland was quoted as saying he was only with United “until the end of the season” and still hoped that he would return to Molde – but Solskjaer has muddied the waters somewhat.
Speaking to Fotballklubben podcast, the 46-year-old said: “I’m not sure how it works. I think the contract is expired and that I’m now under contract with Manchester United. I think we need a new contract there (at Molde).”
Press Association Sport understands that Solskjaer has signed a deal with United until the end of the season and that any return to Molde would be down to the club and manager to agree.
It is believed a manager cannot have contracts with two different teams at the same time. Just weeks before taking the temporary job at United, Solskjaer signed a three-year deal to extend his second spell with Molde.
The Norwegian is the overriding bookmakers’ favourite to permanently succeed Mourinho and leads his side out against Paris St Germain in the Champions League round of 16 on Wednesday. United trail 2-0 from last month’s first leg at February.