The Sun says Russian mega-spenders Anzhi Makhachkala are ready to offer the 30-year-old £200,000 a week.
Anzhi — backed by billionaire owner Suleyman Kerimov — have already handed Samuel Eto'o a monster £350,000-a-week deal.
Now Cole, whose Chelsea contract runs out at the end of next season, has emerged as their latest target.
And the England defender will be sorely tempted by the cash — and the prospect of a four-year contract.
Anzhi's player-coach Roberto Carlos has recommended Cole as his successor at left-back.