Beckham is England's most capped outfield player, having represented the Three Lions 115 times, and sits only behind goalkeeper Peter Shilton on the all-time appearance list.
Meanwhile, Liverpool midfielder Gerrard will reach a century of caps when he captains England against Sweden on Wednesday.
However, the 32-year-old is focusing solely on 2014 World Cup qualification rather than earning the further 16 appearances that would see him surpass Beckham's total.
He said: "David's a hero of mine and he was certainly someone who I looked up to. I enjoyed a lot of my England caps playing alongside him and it's not really very important to me whether I beat David's record or not.
"My main focus is to get this team to qualify for the next big tournament."
Roy Hodgson named his starting lineup for the clash in Stockholm on Tuesday evening, confirming that Gerrard will start after shaking off a knee concern.