Leicester manager Brendan Rodgers (AFP)
Rodgers is believed to be one of the leading contenders to replace Solskjaer if the under-fire Norwegian gets the sack.
United travel to Watford on Saturday with Solskjaer desperate for a victory after his side's lacklustre defeat against Manchester City before the international break.
That loss came hot on the heels of a humiliating 5-0 home thrashing at the hands of bitter rivals Liverpool, leaving Solskjaer fighting to save his job.
Rodgers, who led Leicester to FA Cup glory last season, was asked whether he would be interested in taking over at United during his press conference on Thursday ahead of Leicester's clash with Chelsea this weekend.
"There's two things. Firstly it is really disrespectful to ask the question when you have a manager in place, a good manager and a good man, who is working hard at the club," Rodgers said.
"Secondly I can't really comment on it, because it is not something that is real.
"I am here as the Leicester City manager, proud to be here, privileged to be here and fully committed to the players, the club, the ownership.
"That's about it, all the other noise around that is something we can't control."
It is not the first time Rodgers has been the subject of speculation over other jobs during his spell at the King Power Stadium, having been linked to Arsenal, Tottenham and Newcastle in recent years.
While the gossip does not bother him, he says it can have a destabilising effect.
"It doesn't frustrate me because my focus is always looking for the next game. The only club I am thinking about is Chelsea and getting ready for that," Rodgers said.
"It is frustrating for our supporters and also my players, if anyone is to read anything that is out there then that can destabilise.
"It is something that is the modern game, lots of speculation and gossip, it's all part of the modern game but it's not something I have any focus on."
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