According to the Express, Manchester City are interested in signing Cole and are prepared to offer him £130,000-a-week - £50,000 more than his current wage packet.
Related ArticlesHiddink faces defensive headachePremier League actionAncelotti speaking Chelsea's languageHiddink hails brave CechChelsea lose ground in title racePremier League team newsIn a bid to stave off any other interest, Chelsea will open talks with the England international this summer, but Cole insists the club need not worry about him being lured away.
"I'm at Chelsea, and it's a new chapter in my life," he said. "Hopefully I can win a few more trophies here and that will make it even better.
'Since I've been at Chelsea, I've had a great time and won a lot of trophies. But I want to win a lot more in the future with Chelsea.'
Meanwhile, Cole's captain John Terry has leapt to the defence of goalkeeper Petr Cech who has come under fire in recent weeks following a series of under-par performances.
Hailing the Czech's record this season, Terry said: "For all those people who have had a pop at Big Pete recently - just a reminder.
"We have let in fewer goals that any other Premier League side this season - he will do for us.
"Petr is our mate. He's the best in the world and when he comes out in the last minute at Wembley and gets through a crowd of players to punch the ball clear - we love him."