Striker Cole joined fellow England internationals Rob Green and Scott Parker as part of the Hammers' 26-man squad that travelled to Switzerland on Friday for a six-day training camp.
The 27-year-old has been linked with a move to the Potters since the Hammers' relegation from the Premier League and a deal could now be completed, for an initial fee of around £4.5million.
Coates said: "Cole's a player the club is interested in and Tony Pulis has liked him for a long time, we think he's a very good player.
"It's not done and dusted but it's work in progress.
"He's a player the club is interested in and Tony Pulis has liked him for a long time, we think he's a very good player."
QPR were also thought to be monitoring Cole's availability but he could now be set for a move to the Britannia Stadium, which may end Pulis' pursuit of Birmingham forward Cameron Jerome.
Meanwhile, Coates has admitted free agent Woodgate is interesting the club, with a view to a play-per-play deal being offered to the England international.
The former Middlesbrough, Leeds, Newcastle, Real Madrid and Tottenham defender's career has been plagued by injury.
Coates added on talkSPORT: "We're working on that and it's something we're prepared to do.
"It's work in progress but we're taking a risk. We hope we'll be able to do something."