Stewart said the Owls' opening bid in the region of £200,000 before the weekend friendly with Huddersfield was "not even worth considering".
But now Wednesday boss Gary Megson, also linked with Norwich striker Cody McDonald who had a successful loan stint with Gillingham last season, is expected to increase the clubs offer after speaking with Chairman Milan Mandric.
Meanwhile rumours in the Midlands have also linked Coventry City with Le Fondre's signature with local reports suggesting a bid is imminent.
Millers Boss Andy Scott spoke at Radio Sheffield's Football Heaven managers forum last evening, saying he still expects Alf to be here for the start of the season when Rotherham take on Oxford this coming weekend.