Gordon's agent Andy Evans says the next move is unclear, with the two parties deadlocked.
Evans told the Sunday Sun: "We have hit a brick wall on this one. The valuation that Hearts have put on Craig has not been met and so Sunderland's bid was rejected.
"Both sides are cooling off at the moment and it is now a question of whether either side budges.
"As things stand, no offer has been accepted so Craig has nothing to consider."