Beckham, who captained England himself during an illustrious playing career, believes that Gerrard's ability to motivate is second to none, and that the national side's younger players will benefit from the 34-year-old's presence.
The 39-year-old played alongside Gerrard when the midfielder himself was a younger member of the England squad, with the pair helping their country reach two World Cup quarter-finals.
“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," Beckham told Sky Sports News.
“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.”
Since Roy Hodgson's side's dismal showing in Brazil, many observers have displayed an opposite viewpoint to Beckham, calling for Gerrard to instead retire from international football.
The 34-year-old insists that he won't rush any decision on his future, with Euro 2016 two years away.
Gerrard will be 36 at that tournament but could draw inspiration from Andrea Pirlo, who was 35 when he took part at this year's World Cup and has suggested he could yet backtrack on his decision to retire from playing for Italy.