The 32-year-old Dawson is reportedly being chased by both Aston Villa and Wolves and is out of contract at the London Stadium at the end of the season.
The Ballon D'awson, as nicknamed by the West Ham faithful, has risen from the emergency back-up defender nobody wanted to playing a key role in the squad during his two season stint. Even getting in the mix in the voting for Hammer of the Year.
His impressive 'never say die' performances in the Premier League and Europe have reportedly seen both Villa and Wolves make bids for the centre-back, and West Ham could be tempted to cash in given his age and contract status.
On whether he would let Dawson leave, Moyes said: "Ideally we wouldn't, but it's probably a much more complicated situation."
He added: "I wouldn't completely say no (to more business), but it might not be yes either. It may not be some people coming in, but may be some going out."
West Ham would need to find a replacement sharpish though, and have apparently already open talks with Polish international Bednarek who has been a mainstay in the Southampton first team sqaud.
The 26-year-old is an experienced Premier League campaigner, having played 153 matches for the Saints across all competitions across six seasons.
West Ham have uncharacteristically been very active in the transfer window signing eight players so far, and Bednarek could be next in line according to The Sun.
Aston Villa were leading the race for Bednarek's signature, with Fabrizio Romano reporting on Friday that the club were 'optimistic' over striking a deal for Southampton defender.
Having already lost to the Irons on the field last weekend, the Villans will be looking to avoid a successive defeat in the transfer market.