The 31-year-old defender will be out of contract at the end of next season, and is yet to receive an offer of a new deal to remain in west London.
Cole had reportedly become disillusioned with life at Stamford Bridge under the stewardship of Andre Villas-Boas.
But, after the Portuguese tactician was relieved of his managerial duties by Blues owner Roman Abramovich on Sunday, it could now prompt the England international to commit his long-term future.
Italian TV station Mediaset claims Cole is a £10million target for the Serie A leaders, and are hopeful of negotiating a deal to bring the full-back to the San Siro this summer.
Milan are in London for their Champions League last-16 second leg clash with Arsenal this evening, and after their dramatic 4-0 victory three weeks ago, are on the cusp of progression to the quarter-final stage.
Chelsea's European inclusion is also hanging by a thread, following their 301 defeat away at Napoli - but there is hope that interim manager Roberto Di Matteo will be able to overturn the deficit when the two teams lock horns again next week.
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