James Tomkins has not travelled with the rest of the West Ham squad for their pre-season tour of America ahead of a proposed move to Crystal Palace, according to Sky sources.
However, Sky sources understand a fee between the clubs is yet to be agreed.
Palace value Tomkins at around £6m, but West Ham are hoping to secure close to £12m for the central defender.
Tomkins, who came through the youth ranks at West Ham, made 32 appearances for Slaven Bilic's side last season.
The 27-year-old featured predominantly at right-back for the Hammers during the 2015/16 campaign, scoring in the FA Cup quarter-final defeat to Manchester United.
Palace manager Alan Pardew is currently shaping his squad ahead of the new season and has already completed the signings of winger Andros Townsend and goalkeeper Steve Mandanda.
Tomkins, who only signed a new five-year deal at West Ham in February 2015, is currently the east London club's second longest serving player behind captain Mark Noble.
He joined West Ham in July 2005 and has made 243 first-team appearances, scoring 11 goals.