The England defender faced a grilling from his Twitter followers on Wednesday afternoon, with many using it as an opportunity to bait the former Arsenal left-back.
But besides describing Ryan Bertrand and Daniel Sturridge as his best friends at Stamford Bridge, Cole admitted that he would have loved the chance to link up with Gerrard at club level.
“Who's the player who didn't join Chelsea you wanted to see him in a chelsea shirt?” asked ‘True Blue’.
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“I think that would be Steven Gerrard, about 5 years ago. Great player for Liverpool & England,” Cole replied.
Gerrard has twice came close to moving to Stamford Bridge - in 2004 and 2005 - but opted to stay at his hometown club instead.
Cole also revealed that he is enjoying the new style of play under boss Roberto Di Matteo following the arrival of the likes of Eden Hazard and Oscar.
“Yeah with the new signings we've got we're playing v attacking fball, so I hope it entertains!” he wrote.
Cole caused controversy in 2006 when he turned down a new contract worth a reported £55,000 a week at boyhood club Arsenal to join Chelsea.
But while he was bombarded with insults from Gunners fans, the 31-year-old admitted that Arsenal legend David Rocastle - who died of cancer in 2001 - was his biggest hero as a child.
He wrote: “David Rocastle. He was a winger like I was and took time to chat when I met him as a kid. I miss him.”