QPR chairman Tony Fernandes says he wants Loic Remy’s future to be decided in the next couple of weeks.
The likes of Tottenham, Arsenal and Liverpool have been linked with the France striker, who spent last season on loan at Newcastle.
There has also been speculation about the nature of a clause in his Rangers contract, which allows clubs in the Champions League to sign him for around £8m while others would have to pay significantly more.
Arsenal have made an approach but appear to have been put off by his wage demands, while West Ham recently made an enquiry.
Newcastle want to sign him on a permanent basis but Remy, 27, is not keen to return to the North East.
Fernandes, who signed the player from Marseille for £8m in January last year, would like him to stay at Loftus Road.
Either way, he wants the situation resolved sooner rather than later.
“I’d like to keep Remy and I think I’ve made that clear, but he has to want to stay,” said Fernandes.
“He’s turned down some clubs. Some clubs have come in and he’s said ‘No, I’d rather stay at QPR’.
“If it’s a club that’s not dissimilar to QPR, then why go? If it’s a club that’s much bigger then I won’t hold him back.
“The decision has to be fairly soon. We don’t want to be without a striker. My position on Remy is that I’m not going to wait until two days before the transfer window [closes].
“I signed Loic and he did a great job for QPR and for Newcastle. I don’t think he would only stay for the money. He wants to be France’s top striker and believes in his ability.”
Remy is due to report for training when he returns from holiday, while Adel Taarabt is already training with Rangers after also ending last season on loan, at AC Milan.
Brazil goalkeeper Julio Cesar, who ended last term on loan at Toronto, is likely to cut his ties with Rangers, but the future of Taarabt – the star of the 2010/11 promotion-winning campaign – is less certain.
“I would like him [Taarabt] to stay because he’s had a great history with us,” said Fernandes.
“He’s never done it in the Premier League – he’s done it in flashes – but he is probably one of the best players I’ve ever seen.
“But it’s up to him – whether he wants to do it or not. From a professional standpoint I think it would be great if he stayed.
“But I only want players who want to get out there and play for us. That’s my message.”