The France international only moved to Loftus Road in January, but his six goals in 14 appearances over the second half of last season were not enough to keep QPR in the Premier League.
As a proven performer at the highest level, the 26-year-old was expected to be among those on the move this summer.
Numerous clubs have been credited with holding an interest in his services, with Newcastle United manager Alan Pardew admitting to being part of the chasing pack.
No deal has been agreed, though, and Remy remains on the books at QPR.
As he is tied to a long-term contract, Beard maintains that the capital club will only agree to let him leave if a suitable bid is tabled.
He said in the Fulham Chronicle: "It's realistic that everybody with a contract will stay. If clubs come in and it's the right deal for QPR and the player, we'll talk about them going somewhere else.
"Loic Remy is like everyone with a contract. He's a great character, and if we have him playing for us in the Championship he'll score you a lot of goals, but if something happens we'll look at it."