The Mail reports that the Hammers are making early moves for the 23-year-old to ensure a deal can be completed early on once the January window opens.
Swansea have reportedly already rejected an offer of £18m telling West Ham they would only consider offers worth £25m.
Don't get why people are moaning about Alfie Mawson. He is young, which is something we have been crying out for, and he is actually a very good defender.— West Ham Fan Zone (@WHUFCFZ) December 27, 2017
I think he would be a great addition.
The Mail claims the east London club are ready to meet that price tag, with an offer of £20m plus £5m in add-ons on the way.
West Ham, who currently sit in 17th, are in need of competent defenders themselves and the addition of Mawson would potentially fill the cracks that have seen them severely under-perform this campaign.
It remains to be seen whether the offer will pry the defender from Swansea, but with Swansea needing reinforcements themselves, the money offered could be enough to tempt the Swans to sell.
Reports also suggest that 15 percent of any fee for Mawson will go to Barnsley, with the club agreeing the sell-on clause when Mawson moved to Swansea in August 2016.