The 26-year-old arrived at Loftus Road in an £8 million deal in January, scoring six goals in 14 appearances as the Rs finished bottom of the Premier League table.
Remy is thought to be one of the highest earners at QPR but Beard insists only a suitable bid will see the striker depart.
"It's realistic that everybody with a contract will stay," he told the Fulham Chronicle. "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."
Remy has represented France 18 times, scoring four goals, with his last appearance coming in a World Cup qualifier victory over Georgia in March.