6:17PM BST 12 Jul 2011
England forward Cole, 27, is currently in Switzerland with West Ham for a pre-season training camp but us due to hold talks with Stoke City manager Tony Pulis upon his return.
Stoke chairman Peter Coates told Sky Sports: "We have agreed terms with West Ham, that's done. Now it's a case of can we agree terms with Carlton?"
Cole joined West Ham from London rivals Chelsea in July 2006 and scored 42 goals in 165 appearances. But he managed just five league goals last season and is now set to leave Upton Park.
The fee has been reported to be an initial £4 million with a possible £2 million in add-ons.
Coates said Stoke had tried to sign Cole on previous occasions but was optimistic that this time the forward would make his way to the Midlands club, who lost in last season's FA Cup final to Manchester City.