The defender could move to Molineux ahead of Sunday's Premier League trip to Manchester City, Planet sport understands.
Wolves boss Julen Lopetegui has been looking for January reinforcements with his side two points above the bottom three.
He has already signed Atletico Madrid forward Matheus Cunha on loan, ahead of a permanent summer deal, with Paris St Germain midfielder Pablo Sarabia joining earlier this week.
Hammers boss David Moyes was critical of Wolves ahead of their 1-0 defeat at Molineux last week after their interest in Dawson went public.
"I might bid for one of them after the game and see how it goes," he said.
"Is it destabilising? By the way it is, yeah. Let's be fair, Wolves tried to buy Daws in the summer and we said no at that time."
Dawson has been at West Ham since joining from Watford, initially on loan, in 2020 and has made 87 appearances for the Hammers.
He also spent nine years at Wolves' bitter rivals West Brom before leaving for Watford in 2019.