The Blues defender currently earns around £115,000-a-week, but Starsport reports that Chelsea have offered Cole a new deal worth £100,000-a-week on a one-year extension.
Club owner Roman Abramovich is apparently keen to lower the average age of the Chelsea first-team squad, and is believed to be prepared to limit players over 30 to one-year deals.
Chelsea stars Frank Lampard and Ashley Cole both have contracts that expire at the end of this season, and the England internationals have been linked with moves away from Stamford Bridge.
It seems that Chelsea have offered Cole a new deal, but the terms could lead him to explore his options elsewhere. Big-spending Paris St-Germain are thought to be interested in the England defender, while Jose Mourinho at Real Madrid is also a big fan of his former-Chelsea player.
PSG boss Carlo Ancelotti, who also managed Cole at Chelsea, recently described the fullback as "the best left-back in the world."
Cole could win his 99th England cap if he's selected against Poland on Tuesday evening, and the left-back was reportedly the subject of a potential £150,000-a-week contract offer from PSG this week.
The former-Arsenal star has been at Chelsea since 2006, and the 31-year-old has won one Premier League, four FA Cups, one League Cup and a Champions League during his six-year spell at Stamford Bridge so far.