Manchester United chief executive Ed Woodward has reportedly been inundated with interest in the vacant post at Old Trafford from some of the world's top managers.
Solskjaer has won both of his games in charge so far to thrust his name into the reckoning to get the job on a permanent basis, while the likes of Mauricio Pochettino and Zinedine Zidane have also been linked with the role.
Woodward has received interest from some of the biggest names in football, although he insists that a decision will not be made before the end of the season.
Radio host Jim White told talkSPORT: "Ed Woodward told me, on the record, that last week was not a proud one for Manchester United.
"He said the club now needed to undergo the proper process of finding the right manager and that nothing will be announced before the end of the season.
"He said he's been inundated with applications and recommendations – the top people in the game want this job. But he said, at the end of the day, nothing will be announced before the end of the season."
Pochettino is currently the bookmakers' favourite to be named as Mourinho's permanent successor, despite having only signed a new long-term contract with Spurs earlier this year.