Liverpool midfielder Gerrard will be 36 by the time the 2016 European Championship is played in France but is just two appearances short of breaking Beckham’s outfield record of 115 caps for England.
Former England captain Beckham told Sky Sports News: "Obviously I have been there. I played for England for quite a few years and captained England. But it's one of the things I miss out of my whole career.
"I miss playing for Manchester United, I miss playing for Real Madrid, but England's always been my real number one passion and playing for England always meant more to me than anything else. So for me it's the thing I miss - playing for England.
"I think it would be great if Steven continues because it was a disappointing tournament for the whole team and the captain kind of takes the real kind of brunt of things.
"But as a captain you feel a certain responsibility to lift the team. Stevie has done that for many years for Liverpool and for England. He has always been a real motivator, the way he plays and his passion that he shows on the pitch.
"I would love to see Stevie continue because I think these young players need someone to look up to and a mentor - someone that has been there and done it - and I think that Steve is a great captain. He has been for Liverpool and England.
"He doesn't need my advice but one thing that I would say; that if you can play for England as long as you can, then do it."You can see more from the interview with David Beckham on Sky Sports News from 7am on Sunday.
Absolute Cobblers. Beckham is out of touch. Maybe he should have stayed on in England which would have prolonged his International career. Don't be silly Dave. We need a new captain.- lee the gooner