Atsu, who featured for Ghana at the World Cup, joined the Blues last September from Porto but was immediately loaned to Dutch side Vitesse.
Aston Villa, Hamburg and Espanyol are also understood to be keen on the 22-year-old, whose pace and trickery troubled Jurgen Klinsmann's USA before they ran out 2-1 winners in that Group G contest.
But Chelsea boss Jose Mourinho is expected to afford Atsu the chance to impress during pre-season before sanctioning any second spell away from Stamford Bridge.
West Ham have already added striker Mauro Zarate to their ranks and have sought to further boost their attacking options - having scored just 40 goals in 38 Premier League games last term - by lodging a £12m bid for Ecuador forward Enner Valencia.
His Mexican side, Pachuca, have admitted a deal is close but are continuing to press for a sell-on clause.