The midfielder has been open about his desire to return to Marseille, where he spent last season on loan, while some reports have linked him with a move to his boyhood club Everton.
"It would be massive if Joey could stay," Simpson told West London Sport. "Everyone knows what his qualities are. I hope he stays, for me and for the team, because he's a great asset."
Barton joined QPR from Newcastle United in 2011, but was later shipped out to Ligue 1 by then-manager Mark Hughes after picking up a 12-game ban for violent conduct.