The Leicester City manager has been touted as a possible replacement for Ole Gunnar Solskjaer should the Norwegian get the sack at Old Trafford.
The former Celtic boss was asked whether he would be interested in the United role ahead of Saturday's clash with Chelsea, but was not prepared to engage.
He said: "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.
"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 the 48-year-old 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.
"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, but it's not something I have any focus on."