The former Wales international, 34, is out of favour at Derby County and was recently loaned out to Brighton & Hove Albion.
However, Gradi - who is in charge of the first-team at Crewe after Steve Holland was sacked - said it is highly unlikely that Savage will be heading back to Gresty Road in the near future.
"He has links here having played for Crewe early in his career, but I think that's all a bit tongue in cheek and I can't see it happening," he said.
"I don't think it's a job for someone who hasn't got any experience of management or coaching. I doubt if the board would consider someone who is inexperienced in that way."
Reports last week suggested David Platt, also a former Crewe player, had turned down the chance to manage his former side.