Goalkeeper Martyn and Vaughan spent time together in the treatment room during the 2005/06 season before Martyn called time on his illustrious career.
"He (Vaughan) went to the USA for the career saving op on his knee at the same time as I was receiving treatment for a career-ending injury to my ankle," he told evertonfc.com.
"It was a strange comparison. There was me with more than 900 games behind me, and James with barely four or five, both facing career threatening injuries.
"I suppose you could say the outcome was the right one, and the old codger had to call time while James made a full recovery."
Martyn added: "I dearly hope he gets an injury free run now right through to the end of the season, so he can start to live up to that rich potential.
"As he gets older he will probably learn to channel that energy and exuberance differently, but for now his work-rate is refreshingly infectious.
"He can be a spark for the whole team.
"The crowd is lifted when they see him chasing down defenders and getting blocks in, the players around him think ‘maybe I should be doing that, too' and suddenly the whole team performance is lifted."