Dawson, who is now into the final six months of his West Ham contract, is keen to move north in order to be closer to his young family in Cheshire.
The 32-year-old was offered a three-year contract by Wolves during the summer, but a proposed deadline day move fell through when West Ham failed to secure a replacement.
Asked whether Dawson was likely to leave the club this month, Moyes said: "I don’t know but we’ve had an offer from Wolves. At the moment, we’ve not accepted it.
“That’s about as much as we can tell you. No idea [if he’ll leave], not at the moment.”
Wolves have also been linked with a move for Irons striker Michail Antonio, who has been frustrated at losing his starting place to summer signing Gianluca Scamacca.
"We’ve had no offer and no enquiry so I don’t know where that’s grown legs from,” Moyes said. “Nevertheless, Mick’s really important for us. I think he’s got a two-year contract so he’s here for a while.”
Moyes also confirmed that Sevilla forward Youssef En-Nesyri is unlikely to arrive this month, despite the Hammers’ long-standing interest.
West Ham are keen to bolster their forward options before the window closes but in a post on social media this week, the Moroccan expressed his desire to stay with the Spanish side, who are currently languishing in 17th in LaLiga.
"He’s a player we’ve been looking at for a few years, not just recently, but I don’t think he’s coming to West Ham, no,” Moyes added.
“We said in the summer we’d do most of our business then. We might try and do something in January if the right player becomes available but at the moment we’re going with what we’ve got.”