"I can confirm that we had some 'very civil' talks with Chelsea," Arsenal deputy president David Dein told Sky Sports Network on Saturday.
"At the moment there's nothing more to say on that. If something happens we'll see, but at the moment he's an Arsenal player."
In 2004, Chelsea held personal talks with Cole without referring to Arsenal.
The incident saw Cole, Chelsea and their manager Jose Mourinho fined heavily by the English Football Association.
After selling Asier Del Horno to Valencia, Chelsea are looking to enforce their left flank with a new signing, long-term interest Cole tops their list.
Despite admitting Chelsea's inquiry, Dein insisted that the side is unlikely to accept any offer for Cole.
"We will consider selling him only if something happens and an offer is suitable which we wish to accept, until then he's under contract with us," Dein said.