Cole will leave the Hammers in June when his current contract with the Premier League outfit runs out.
The 31-year-old striker scored 68 goals in 293 appearances after first joining the London club from Chelsea in 2006.
Gold has now taken to Twitter to wish the Englishman well as he embarks on a new journey.
Good bye @CarltonCole1 Good luck Carlton in your future endeavours, it's been a pleasure knowing you. dg— David Gold (@davidgold) May 29, 2015
Cole was largely a bit-part player for West Ham in the 2014-15 season, making just 23 appearances in the Premier League.
In those 23 matches, the former Chelsea striker scored two goals and created eight chances, while having a pass accuracy of 58% and a shot accuracy of 46%.
Cole told Sky Sports that he was close to leaving West Ham for Premier League rivals West Bromwich Albion on transfer deadline day in January.
It will be interesting to see which club Cole joins in the summer transfer window.