Midfielder Tunnicliffe has fallen out of favour at Craven Cottage and is reportedly ready to leave next month.
Mark Warburton's Rangers are in the market for midfielders after tearing up Joey Barton's contract in November, while the report describes QPR counterpart Ian Holloway as a confirmed fan.
Tunnicliffe is out of contract in the summer, which would likely put him within the budgets of both Rangers and QPR.
Ryan Tunnicliffe (right) lifts FA Youth Cup with Manchester United
Warburton admitted via the Daily Record on Thursday that, due to often inflated mid-season prices, he is looking to bring one or two loan signings to Ibrox January, and a move for Tunnicliffe could tie in to those plans.
QPR, meanwhile, have tightened their purse-strings significantly since falling out of the Premier League and returning boss Holloway is unlikely to have much money to play around with.
The Daily Record reported on Friday that the R's are targeting a January return for Glasgow Rangers defender Clint Hill, who swapped Loftus Road for Ibrox in July.
Glasgow Rangers' Clint Hill