Reports on Thursday claimed that Cole had been issued a deadline of the last day of the season to agree fresh terms that had been verbally offered to him.
Cole is out of contract at the end of the season and his long-term future at West Ham has been the subject of conjecture.
The 29-year-old has struggled to hold down a regular place in the Hammers side this season with Sam Allardyce preferring to play a system of one striker his starting XI, while the loan signing of Andy Carroll has also pushed Cole down the pecking order
However, Cole's representatives insist there has been no new contract offer from West Ham and they have not heard anything from the club since pre-season.
"There was one offer that was discussed in pre-season after which nothing has been discussed since," read a statement from Cole's representatives to Sky Sports.
"Carlton's only focus has been to do his best for the team to help them stay in the Premier League.
"Carlton is out of contract in the summer and he has always performed at his best whenever he has been called upon."