The 30-year-old has become the nation's highest wicket-taker by surpassing Botham's record of 528 in all formats, but the Lancashire bowler is far behind the former player's Test record of 383.
"I would like to do it but it is not something I think about day to day," BBC Sport quotes Anderson as saying. "The reason I got here is by concentrating on the small things. The spells that I bowl, each ball I bowl and concentrate on wickets and how I take wickets.
"Since I started doing that the wickets have been taking care of themselves. Hopefully I can look back at the end of my career at a couple of records and I can look back really fondly but now I just concentrate on bowling well for England."
Meanwhile, England are preparing for the second one-day international against New Zealand following their opening defeat on Sunday.