Rangers have slipped back into the Championship after only a two-year stint in the Premier League and manager Harry Redknapp has admitted he wants to offload a number of his players.
Mbia only joined QPR from Marseille last summer, but it appeared that he contacted Joey Barton, who moved to the Ligue 1 club as part of the deal, to suggest they swap clubs.
A public message sent from Mbia's account read: "So... Seriously @Joey7Barton do you want rechange your seat with me? #qpr #om"
Ian Taylor, the club's head of media and communications, said he had spoken to Mbia and released a statement via the social networking site.
It read: "The club is aware of tweets from the official Twitter account of #QPR midfielder Stephane Mbia today
"Stephane Mbia has informed the club he is not responsible for these tweets.
"The club will continue to investigate and deal with the issue internally."
Mbia has since told The Guardian: "I do not know how this happened. Someone must have got hold of my login and password because I did not write these things.
"This was not me. I did not write the tweets, and I have made people at the club aware of that.
"I saw the messages this morning and spoke with the club about them, but now I see there are more appearing in my name."
Barton responded to the tweet by calling on QPR's players to pull together after their relegation.
"How do I answer this politically? Er...Nope #allezLOM," he replied.
"If you go down with a team, you should stay and help them up mate. They need you all to stick together and help them back."