Taylor, who replaced another ex-Claret in Steve Cotterill during the summer, was given the axe after losing seven of his last eight games.
Former Shrews boss Paul Hurst is currently the 2/1 favourite to return to the role, second-favourites Dean Holden and Michael Flynn are tied at 4/1. A Burnley favourite is also said to be in the running.
According to BonusCodeBets, these are the latest odds for the Shrewsbury vacancy:
1 / 4