The 28-year-old is deemed surplus to requirements at Stamford Bridge, with both Ben Chilwell and summer signing Marc Cucurella ahead of him in the left-wing back pecking order.
The Hammers were understood to have walked away from talks with Emerson and his representatives last week after failing to agree personal terms.
However, West Ham have since re-entered negotiations and journalist Fabrizio Romano claims that there is a full agreement between both clubs and the player over a permanent transfer to the London Stadium.
Romano adds that the East Londoners are set to pay an initial £13m plus a further £2m in add-ons, and the Italy international has agreed to sign a five-year contract until June 2027.
Emerson is now allegedly set to undergo the first part of his medical on Monday night before an official announcement of his arrival at the London Stadium can be made.
David Moyes is on the lookout for a new attack-minded left-back as 32-year-old Aaron Cresswell is currently the only senior option at his disposal.
After starting only eight games in all competitions for Chelsea during the 2020-21 campaign, Emerson was sent out on loan to Lyon where he received regular first-team football.
The 27-cap Italy international, who can play as either a left-back or left wing-back, made 36 appearances for Lyon last season, but the French side opted against signing him on a permanent basis.
Emerson is now set to become Moyes's seventh signing of the summer window, following the arrivals of Alphonse Areola, Nayef Aguerd, Flynn Downes, Gianluca Scamacca, Maxwel Cornet and Thilo Kehrer.
Meanwhile, the Hammers remain interested in signing Club Brugge midfielder Hans Vanaken, who has publicly expressed his desire to move to the London Stadium.
The 29-year-old has spent his entire club career in his native Belgium and believes the opportunity to join West Ham at this stage of his career is too good to turn down.
"Clearly there is interest, enough has been written about it. New talks tomorrow and we'll see where it ends," Vanaken told reporters last weekend.
"I think it could be my last chance and I want to do it. There's still a lot to talk about, let's wait and see."
Sky Sports News claims that West Ham have seen a bid of €10m (£8.5m) rejected by Club Brugge for the Belgium international, who has recorded 101 goals and 72 assists in 342 appearances for the Blauw-Zwart.