The ex-midfielder turned BBC Sport pundit, 40, spent five years at Leicester and three at Derby but never turned out for Yorkshire side Leeds.
During a Q & A on Twitter, however, Savage singled Leeds out as the one club he would have liked to play for but didn't during his long career.
Meanwhile, when it comes to Premier League sides who would rather not be in the Championship next season, as opposed to those already in the division, Savage also picked the three teams he feels will be relegated from the top flight this term.
The 40-year-old picked one of his former sides in Leicester, while also choosing the two other clubs to have been promoted last campaign:
What an intriguing prospect Savage turning out for Leeds would have been, though, although fans will never know what could have been.
They perhaps wouldn't have been getting any flair from the Welshman - but they certainly would have got a tough tackler.