Mutch, 23, joined QPR from Cardiff last summer, but has made little impact at Loftus Road, and reports last week suggested that Crystal Palace wanted to bring him to Selhurst Park.
New manager Alan Pardew has already snapped up Arsenal striker Yaya Sanogo on loan for the rest of the season, and is still looking to add to his squad before Monday's transfer deadline.
Sky Sports suggested that QPR rejected Palace's loan bid for Mutch last week, and were looking to recoup most of the £6m they paid for him just six months ago.
That appears to be a little too rich for Palace's blood, and now QPR have made an offer to the Eagles in a bid to secure a deal.
The R's have reportedly asked Palace to send Fraizer Campbell to Loftus Road in a swap deal for Mutch, according to West London Sport.
Campbell, formerly of Manchester United, is a former team mate of Mutch having played together at Cardiff last season, but could now be used as bait to land the ex-Birmingham midfielder.
The 27-year-old has scored three goals in 17 Premier League appearances, but has played just three minutes of Premier League football since Pardew took over at Selhurst Park.
His departure could release some funds for Pardew to sign another striker, and whilst Palace seemingly haven't answered the proposal yet, this is a deal to keep an eye on.