Keane and Ian Wright were paired up against Sky Sports punditry duo Gary Neville and Jamie Carragher for an end-of-year quiz on The Overlap podcast.
With Keane struggling to answer a question on who out of David Moyes at Everton or Emma Hayes at Chelsea was the longest-serving, the Irishman grabbed his phone and joked: "I might call Joey Barton. Joey would know."
Ian Wright then dialled up Emma Hayes herself to confirm she had been at Chelsea for longer.