How would the 36-year-old have fared at the Scottish champions?
Indeed, when asked on social media by a follower if there was a club he could have signed for but didn't and whether he regrets it, the former midfielder named the Scottish champions.
The 36-year-old enjoyed a career that took him to a great number of different clubs, although he never made the move north to Scotland.
Injury impeded him at a number of those sides and Bullard hints that the 'magic sponge' again played its part in him not joining up with the Bhoys.
@jimmybullard Jimmy is there a club you could have signed for but didn't? Maybe regret it?— Daniel Povey (@Povey1990) August 23, 2015
Bullard is known more as an entertainer now than he is a former footballer - but he certainly had a superb range of passing and eye for a sensational strike back in his playing days.
All eyes for Celtic now will naturally be on Tuesday night's Champions League play-off second leg against Malmo. Will the Bhoys do what they couldn't manage last season and make it to the group stages? They have a 3-2 lead going into the return leg.