The 32-year-old midfielder, who made his international debut against Ukraine in 2000, earned his 100th international cap in the friendly defeat by Sweden in November but is still 15 short of Beckham's high for an outfield player.
"My personal ambitions are to get as many caps as I can - I have got David Beckham's record in my sights, so I am going to try to beat that because he is a special player," said Gerrard.
If he remains fit, Gerrard could close in on Beckham's tally at the 2014 World Cup in Brazil.
The Three Lions currently sit second in qualifying Group H, two points behind Montenegro, who they face in March shortly after a trip to San Marino.
Gerrard feels Hodgson's squad should not only be confident of qualifying but making a major impact at the tournament.
"I don't want to raise expectations, I am sure it will probably go through the roof if and when we get there, so I don't really want to talk about the World Cup until we actually get there, we still have some important games to play, but I am confident we can achieve it (qualification)," Gerrard said.
"As I always say going into a major tournament, you need to get that bit of luck and when the ball drops your way, I think you can achieve the impossible - I have done it before with Liverpool, and we have seen Chelsea do it last year (in the Champions League).
"It is not necessarily all the time that the best teams win these competitions, so we can go into there with hope and belief."