Asked about the rumours linking him with a move to Old Trafford, Rodgers said: "I don't take it as anything, it's not real.
"There's always gossip and that will be there until they appoint a full-time manager.
"My commitment is to here. The culture here is about the development of the players, and that's where I see it, even more so in this period."
PSG are reluctant to lose Pochettino midway through the season and have rebuked United's contact to discuss a possible compensation deal.
United are therefore expected to push forward with their plans to appoint a reputable caretaker manger until the end of the season.
They have made contact with former Barcelona coach Ernesto Valverde.