Both players' deals are up at the end of this month and the future of Cole in particular has been the subject of increasing speculation.
The 28-year-old, who is part of England's World Cup squad in South Africa, has already been linked with Manchester United, Liverpool, Arsenal, Manchester City and Tottenham.
As negotiations over a new contract at Stamford Bridge dragged on, it became increasingly likely Cole's seven-year stay would come to an end.
Manager Carlo Ancelotti had repeatedly stressed his desire to hang on to the midfielder but behind the scenes the parties could not reach an agreement.
Cole has been reluctant to discuss the situation in public but in March he confirmed talks had broken down, saying: "We can't seem to find common ground and it's distracting. At the moment there is no offer on the table, so I know where I stand."
Chelsea's stance is also likely to have been influenced by Cole's failure to hold down a regular starting spot this season.
The Londoner had been a key player in the rise of the club under owner Roman Abramovich but a serious knee injury suffered in January 2009 put him out for eight months and on his return he struggled to rediscover his best form.
Cole arrived at Stamford Bridge in a £6.6million deal from West Ham in the summer of 2003 and helped the Blues win their first Premier League titles under Jose Mourinho in 2005 and 2006.
Arguably Cole's best season for Chelsea came in 2007/08, when he picked up the club's Player of the Year award as they finished just behind Manchester United in the league and also lost the Champions League final to their rivals on penalties.
The last of Cole's 40 goals in nearly 300 appearances came in the 2-1 win over Manchester United in April that all but sealed a third Premier League triumph, while he also picked up three FA Cup winners' medals and two League Cup titles.
A move to another London club is likely to be appealing to Cole and Spurs manager Harry Redknapp yesterday confirmed he is interested in signing the midfielder.