Skysports.com understands QPR are lining up a bid to bring Quashie back to Loftus Road, where he started his career.
"There hasn't been any contact from the club (QPR) so far, but the scenario at West Ham needs to be sorted out first," Quashie told skysports.com.
"I reckon it is just a matter of time before I move on, but whether that will be going back to QPR is another thing.
"It is a club that I love and where I started out as a kid, so it is a club close to my heart. I still try and go to watch them play as often as I can and have been a supporter since childhood.
"The club means everything to me and so to be linked with them is a great feeling. I know what the supporters want there because I am a fan myself, so it is a fantastic football club and I'd love to see an offer from them on the table."
The 31-year-old is keen to get his future sorted out, but understands the Hammers' current worries are far greater than his own.
He added: "I'm just in the process of speaking to West Ham in respect to my long-term future.
"If that means leaving the club then so be it, but there is a lot of speculation at the club in the moment in terms of takeover bids etc, so I'm just going to have to be patient with that.
"The club is going through a transitional period at the moment and my future isn't at the top of their priorities at the moment."