Gerrard donned the captain's armband as England failed to progress from Group D in Brazil - claiming a solitary point to finish bottom behind Costa Rica (seven points), Uruguay (six) and Italy (three).
The 34-year-old Liverpool midfielder is in the twilight of his career and manager Roy Hodgson could opt for a younger captain as he revamps his squad ahead of England's UEFA Euro 2016 qualifying campaign.
"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."
