Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Rigg joined the Barclays Premier League strugglers from Manchester City last season to renew his partnership with then Rangers boss Mark Hughes.
But following Harry Redknapp's appointment as Hughes' successor last month the club have opted for a further change.
They confirmed Rigg's departure in a brief statement on their website that said: "Queens Park Rangers Football Club can confirm that it has been agreed that Mike Rigg will leave his position at Loftus Road."