The former Bournemouth boss has been heavily linked with a move to Parkhead in recent weeks, but a deal to take him to Glasgow eventually collapsed and instead the Hoops sought to appoint ex-Australia manager Ange Postecoglou.
Reflecting on the situation, Jordan argued that Howe had missed out on a big opportunity to resurrect his career.
“I think Eddie Howe should have run up there and I think he’s a coward for not doing it,” he told talkSPORT.
“Celtic got Brendan Rodgers when he was at a stage of his career where was going to rebuild because his reputation had been demolished at Liverpool and people were ridiculing his achievements.
“He was outed at Liverpool and went to Celtic to rebuild his reputation and the first opportunity he’s got to get a bigger job he’s gone to the Premier League to manage Leicester City.
“Eddie Howe should have gone to Celtic, he should have bitten the arm off to take that job because it’s a huge job with huge opportunity.
“I think it was too big for him and I think he’s quite cowardly for not taking it.
“Undeniably, Celtic are a enormous football club with an enormous fanbase, but that fanbase can only be monetised to a certain level.
“You are not going to have the pull or the economics to pull these managers, these big, big name managers into Celtic.
“That’s why people like Eddie Howe, who are peripheral Premier League managers, might have been indexed, rather than bona fide, top drawer managers.”