A glut of Premier League clubs are thought to be in for Austin, with Aston Villa, Newcastle, Southampton and West Ham among the clubs linked.
Crystal Palace seemingly conceded defeat in the chase for the 26-year-old on Wednesday, but Austin will remain in demand through the summer.
QPR boss Ramsey has admitted that their have been offers for his prized asset, but insists he could remain at the club this summer.
“There have been offers,” Ramsey told Sky Sports News HQ. “A player of Charlie’s ability, there will always be speculation.
“At the moment, there has been nothing concrete. We’ve had offers that we’ve rejected, and we’ve had offers that Charlie himself has not been happy to take on.
“At the moment, he’s a QPR player and he’s working hard in training. I’m having the idea that he will be here into the season. If he is here during the season then he is going to be someone that we want to use.”
Austin, who scored 18 Premier League goals last season and earned himself an England call-up, said last week that h would be happy to remain in the Championship with the Rs.