The 84-year-old Ecclestone has been at the helm of F1 since 1978 and has overseen dramatic growth in the sport which has led to F1 becoming firmly established as the pinnacle of motorsport.
However, it has not all been smooth sailing of late, with the Briton having faced bribery charges in Germany and currently trying to turnaround F1's ailing viewership figures.
Earlier in the week, it was announced that a US-Qatar partnership involving RSE Ventures, which is headed by Stephen Ross, the owner of NFL franchise Miami Dolphins, and Qatar Sports Investments, the Middle Eastern firm which owns French football club Paris St Germain, is looking to buy a controlling stake in F1 from private equity firm CVC Capital Partners. Jordan believes that this is the perfect opportunity for Ecclestone to step aside and allow new blood in.
"I think he's done a remarkable job but time has played its role and he should go," Jordan told BBC Radio 5 live.
"We need to leave it for the next generation in a better state. He has to keep asking himself that and where the timeframe is for him to leave. I think it's now."
He added: "The man is a legend. He has taken the sport from absolutely nowhere but, at the end of the day, he's not immortal. He may think he is but he's not.
"There are times you have to say 'look, I've done everything that I can do'.
"It does need somebody radical in there who is going to really shake it all about and go back to basics."
However, even if there is a change of ownership, former FIA chief Max Mosley says that he does not believe that this will change Ecclestone's position.
Speaking to the BBC, Mosley said of Ecclestone: "He is the person who has managed to sell it [F1] everywhere. I am sure CVC have had thoughts about an 84-year-old chief executive. There is nobody else who does the job as well."
Mosley added that Ecclestone's position "won't change" if a takeover goes through.