Jordan believes the 84-year-old, who has been in charge since 1978, should allow "somebody radical" to take over.
F1 owners CVC Capital Partners and RSE Ventures, working with investors from Qatar, are in talks about a takeover of the sport.
"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."
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RSE Ventures is headed by Stephen Ross, the owner of NFL franchise Miami Dolphins. They are planning a bid for CVC's 35.5% controlling stake in the holding company that owns F1.
Ecclestone's position at the head of F1's commercial arm has come under scrutiny in the past year - he fought bribery charges in Germany while there have been concerns that the sport is losing its appeal.
While acknowledging how Ecclestone had grown F1, Jordan welcomed the possibility of new people running a sport which is "going through a bit of a dip".
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."
Max Mosley, the former president of motorsport's governing body the FIA, told 5 live on Wednesday that Ecclestone's role "won't change" if a takeover of F1 is completed.
Bernie Ecclestone should step down as Formula 1 supremo, says BBC chief F1 pundit Eddie Jordan.