Cole is being probed for allegedly flicking a V-sign at an Arsenal fan on Sunday. But Soho Square insist that there is no video evidence of the incident.
Still photos clearly show Cole responding to taunts but the FA are unable to proceed unless they have the evidence on tape.
Cole, 26, suffered intense and persistent taunting throughout the Blues' 1-0 defeat.
He reacted only after the match when he was heading for the tunnel at the Emirates Stadium.
Historically, any gesturing which is viewed as a possible incitement to fans has been punishable with either a ban or heavy fine.