The 33-year-old is out of contract at Stamford Bridge this summer and is yet to be offered a new deal, while the Nigerian has been sidelined by the impressive Nemanja Matic.
The Portuguese boss is eager to keep the 33-year-old but Blues owner Roman Abramovich has yet to sanction a new deal, prompting Cole to explore other options.
After watching his struggling Milan side record an underwhelming victory over Catania on Sunday, Seedorf spoke of his desire to strengthen his squad in the fullback positions.
"I'd prefer the likes of Cafu and Serginho on the flanks, but we don't have them!" he told reporters.
"[Daniele] Bonera has brought great balance to the side, [Kevin] Constant is a midfielder, [Urby] Emanuelson has played as a fullback a few times in his career, but we don't really have a left back."
Mikel is also a target, but any move for the Nigerian this summer depends on whether Milan decides to sign Valencia loanee Adil Rami and QPR midfielder Adel Taarabt on permanent deals.
Should the club not, the Rossoneri will free up somewhere in the region of 14 million euros to use in their pursuit of Mikel, who moved to Stamford Bridge from Lyn Oslo in a deal worth 19 million euros in the summer of 2006.
Milan and Chelsea remain on good terms, having successfully negotiated the transfer of Michael Essien to San Siro for an undisclosed fee in January.