The Sun says he is now pushing for a start at Swansea on Tuesday after impressing as a second-half sub in Wednesday's 3-2 home defeat by Sunderland.
But he is still on course to leave the Hoops in January with Paris Saint-Germain his preferred destination.
Taarabt almost joined the French club in August but the move collapsed when they would not meet Rangers' £13million asking price.
The west Londoners refused to budge on the valuation because they have to pay a 40 per cent sell-on fee to his former club Spurs.
But with Air Asia tycoon Tony Fernandes now owner at QPR they may take a bid as low as £9m.