The 33-year-old's current deal expires at the end of the season and the Stamford Bridge club want the left-back to accept a reduction on a salary worth in excess of £150,000-a-week
The England international's current deal expires at the end of the season but the Blues want him to accept a reduction on his salary, which is heavily incentivised and worth more than £150,000 (€180,000) per week.
Discussions have been held with Chelsea chiefs and the 33-year-old and his representatives are understood to be relaxed about the situation, in the knowledge that there will be no shortage of offers in the summer.
Cole's priority is to stay at Stamford Bridge and boss Jose Mourinho has publicly declared his desire for the left-back to sign a new deal.
"I think, even if you're not playing every game and are not first choice, like he has always been, it does not mean you are not in well condition or deserving of a new contract," said the Portuguese in December.
Cole has found himself in and out of the Chelsea side this season, starting just 11 of the club's 20 Premier League fixtures so far.
The Blues have been strongly linked with a move for Southampton star Luke Shaw, who is considered a perfect like-for-like long-term replacement for Cole.
Unless the England veteran lowers his demands, his time at Stamford Bridge could come to an end this summer, with the former Arsenal man now allowed to talk to foreign clubs.
MLS side New York Red Bulls and big-spending Paris Saint-Germain have previously shown interest in Cole, who is now in his eighth season at Stamford Bridge and has made more than 300 appearances for Chelsea.
He has won nine trophies with the Blues, including the Premier League title in 2010 and the Champions League in 2012.