Striker Austin was widely expected to leave Loftus Road this summer following Rangers’ relegation from the Barclays Premier League.
Newcastle, Tottenham, Everton and West Ham have been linked with the 26-year-old, who scored 18 top-flight goals last season, but the only concrete bid so far has come from Leicester.
Therefore Austin remains at the club with only three weeks of the transfer window remaining and started their 2-0 Championship defeat at Charlton on Saturday.
And Rangers’ director of football Les Ferdinand says that unless the club receive the right offer they will propose an extension to Austin’s current deal, which has a year left to run.
“The fans are waiting for the window to close and are hoping Charlie is still here,” Ferdinand told the Evening Standard.
“These things always seem to drag on, but from the club’s perspective you want it resolved as quickly as possible.
“All he can do is be professional, which he was against Charlton on Saturday. He’s got into this position where clubs are interested in him because he’s been professional and scored goals. He can’t allow himself to slip now.
“The price is still £15million and the only firm bid that has come in is still from Leicester. Everyone feels that bids are going to come in for him, it’s just a matter of when. But if a club doesn’t pay the fee, then we will offer him a new contract to get him to stay.”