City have been linked with the Hammers' England striker as a potential replacement for out-of-favour Stoke forward James Beattie.
However, one stumbling block could be the apparent £15million price tag placed on Cole.
Coates told the Sentinel: "We won't be paying £15million for anyone, unless someone paid that for one of our players.
"We are looking for players and there will be players coming in and out, which is normal. Our objective is to start the new season with a stronger squad.
"I wouldn't rule any player in or out, football is a funny game. Carlton Cole is a very good player. We will have to wait to see how things develop."
Source: Team Talk
Source: Team Talk