Wolves tried to sign Dawson last summer, with the centre-back keen to move north in order to be closer to his young family in Cheshire.
The centre-back was offered a three-year contract but the transfer fell through on deadline day as West Ham failed to sign a replacement in time.
Dawson was not considered for selection for that game, with manager David Moyes admitting the approach had destabilised his preparations.
The 32-year-old, who is into the final six months of his contract, is now expected to join the Midlands club, though it is thought the deal is unlikely to be completed in time for him to face Manchester City on Sunday.
The Irons could seek a loan replacement before the window closes at the end of the month but Moyes has suggested that he is happy with his centre-back options.
Kurt Zouma is fit again after undergoing knee surgery during the World Cup, while Nayef Aguerd, Thilo Kehrer and Angelo Ogbonna are all available.