The former Bournemouth boss was Celtic’s primary choice to succeed Neil Lennon in the dugout but talks between him and the club broke down.
Celtic shifted attention to the next candidate in line and found their man in Australian Ange Postecoglou, with him putting pen-to-paper on a 12-month rolling contract at Parkhead on Thursday.
Jordan has insisted Howe should have jumped at the opportunity to manage Celtic when they offered him the job, as it would have been the perfect club to raise his reputation.
The ex-Crystal Palace owner labelled Howe a coward for not taking over the Hoops, and feels managing the Glasgow giants might have been too big of a job for him.
Jordan told talkSPORT: “Brendan was going to rebuild because his reputation was demolished at Liverpool and people were ridiculing his achievements and he was outed at Liverpool and went to Celtic to rebuild his reputation.
“And the first opportunity to get a bigger job, he has gone to the Premier League and managed Leicester City, after he rebuilt his reputation on the back of his achievements at Celtic.
“Eddie Howe should have gone to Celtic; he should have bitten the arm off to take that job because it is a huge job with huge opportunity.
“And I think it was too big for him and I think he was quite cowardly for not talking it.”
Howe remains unemployed at the moment while Postecoglou has a tough task on his hands with Celtic currently witnessing a sea change on the pitch and behind the scenes.