It followed the pair taking part in a table tennis football match on BT Sport with Sutton misplacing an effort which was celebrated wildly by the ex-Wales international.
Savage took to Twitter to poke fun at the Englishman, asking him “Was this the standard of Scottish football when you played mate”.
Sutton hit back amusingly, much to the delight of thousands of Twitter users.
He said: “The standard of Scottish Division 3 was high when you offered to play for Rangers for free and they didn’t want you...”
Savage, who played most of his career with Leicester City, Birmingham City and Blackburn Rovers, had offered his services to Ally McCoist when the Ibrox side were playing in the fourth tier.
The jibe has been shared more than one thousands times and liked by more than 11,000 people.