Stoke have been trying to add some natural width to their team and have spent much of the summer pursuing a deal for Liverpool’s Oussama Assaidi, who spent last season on loan at the Britannia Stadium.
Manager Mark Hughes admitted his interest in signing Nathan Redmond from Norwich City earlier this week but seems now to have opted for a move for Moses.
The 23-year-old spent last season on loan at Liverpool but struggled for game-time, starting just six Premier League matches for the Merseysiders, scoring two goals.
Born in Nigeria, the wide player began his career at Crystal Palace before joining Wigan in 2010, where he played under current Everton manager Roberto Martinez.
Moses moved to Chelsea two years ago for a fee of £9m and has scored 10 goals in 43 appearances for the west London side.
The Nigeria international represented his country at this summer’s World Cup in Brazil.