The Potters were persistently linked with the England striker, although boss Tony Pulis rebuffed that the club was lining up an offer after reports that a £9million bid had been made last month.
But now Stoke assistant boss Dave Kemp has admitted their interest ahead of the crunch bottom-of-the-table clash with the Hammers at the Britannia Stadium on Saturday.
He told The Sentinel: "Yes, he was there (among targets).
Kemp has praised the attacking prowess of Cole, believing the Potters must be wary of the Hammers, despite four successive league losses for Avram Grant's rock bottom side.
He added: "People say West Ham are bottom, but they've got Carlton Cole for a start and a lot of other very good players.
"We know he can be a big threat for us and we know West Ham as a team will be a big threat."
The Potters secured their first league points of the season with the welcome 2-1 home win over Aston Villa on Monday.
Pulis was expected to miss the game as he mourned the loss of his mother earlier in the day but the Potters boss turned up to deliver a stirring message during the break which helped Stoke come from behind to win.
Kemp admitted: "Football is a big confidence thing. You have to know when to give them a cuddle and when to give them a kick up the backside."
The assistant boss added it is also a balancing act with players who are not in the first team and want to be playing.
The strength of the club's squad was shown when Turkish hot-shot Tuncay could not even make the bench on Monday and Kemp admitted the management team have to work hard to try to keep everyone happy.
He added: "It's a question of man management. I'm not one for going around putting my arms around people a lot of the time.
"But yes, you do have to be ready for certain situations and know when a player might need that arm around him.
"I will speak to them and the manager will speak to them. But the bottom line is, whatever you say to them, players want to be playing. Or at least they should do.
"It's up to us as a management team to manage that kind of situation and hopefully we are doing that."
Source: Team Talk
Source: Team Talk