"He is available for transfer," Simon Grayson told BBC Radio Leeds: "We do not want to run the risk of losing him on a free.
"We have made a stance. There will be no more improved offer of a contract for Bradley."
But Grayson still intends to use Johnson, who has hit three league goals in 17 appearances this season.
"It doesn't mean he's not going to figure for the club," added Grayson, who revealed that talks are still ongoing with two other out-of-contract Leeds players Lucciano Becchio and Neil Kilkenny.
"If he's good enough to play in the team he will. He will give 100 per cent commitment to the club. He's entitled to do what he's done but so are we in what we have done."