Austin has been heavily linked with a move to Newcastle United, with QPR believed to be holding out for around £15m for the former Burnley striker.
Ramsey told Sky Sports News HQ on Thursday there had been offers for Austin – and he concedes it may be difficult to keep his star striker.
“We have to be realistic,” Ramsey told Talksport. “It’s unlikely he’ll stay. We want to keep him but it’s unlikely.
“The club is in a financial position that it needs to recoup some money and I think for his ambitions he wants to keep playing in the Premier League to go to the Euros.
“We’ve been offered £12m and turned it down so we’re looking in excess of £15m – goalscoring is something you can’t coach, it’s just a habit that some people have.”