The topic of Fish's new ranking will be off limits, he said.
Fish claimed the top U.S. spot for the first time Wednesday by reaching the semifinals of the Sony Ericsson Open when he beat No. 6 seed David Ferrer 7-5, 6-2.
The 29-year-old Fish will climb to at least 11th, a career best, in the next world rankings. Roddick, a good friend since childhood, will fall from eighth to 14th after losing his opening match last week.
"I don't think I would ever feel like I was the No. 1 American," Fish said. "Andy has had a pretty good career. You can put his career on top of mine about six times. He's always going to be the top dog in my generation."
But Fish is the lone American with a shot at the title this weekend. He'll try to continue his best run in 10 appearances at Key Biscayne on Friday against No. 2-seeded Novak Djokovic, who is unbeaten this year.
Djokovic extended his winning streak to 24 consecutive matches by defeating forner University of Illinois star Kevin Anderson 6-4, 6-2. Djokovic won two Davis Cup matches in December, and his 22-0 record in 2011 is the best to begin a year since Ivan Lendl started 25-0 in 1986.
"When you watch him play, it's really not that surprising that he hasn't lost yet, because he's playing so well," Fish said. "He's not going to win every single match this year. Whether it be this week or in July, he's not going to win every one. It's just not possible. So hopefully it can be against me."
As Djokovic closed in on his latest win, he unveiled his version of the Petko Dance -- a celebratory jig introduced by Andrea Petkovic. Petkovic and Djokovic were both born in Serbia.
Fish was braced for an endurance test against Ferrer, a dogged baseliner, but the Spaniard had back-to-back double-faults to lose serve and fall behind 6-5 in the first set, and Fish pulled away from there.
Ferrer, who lost just 12 games in his first three matches, said he was bothered by indigestion.
"A lot of pain in my stomach," he said. "In the second set, I cannot run anymore."
Fish thrived in the role of front-runner, winning the final 15 points on his serve. In the past two matches, he has lost only 11 of 84 points when his first serve was good.
"I've served well over my career," he said. "To be confident enough to not have to press is key."
The afternoon crowd was subdued -- there were no chants of "USA!" -- but Fish's rooting section did include golfer Sergio Garcia of Spain, even though Ferrer is Spanish.
"Sergio and I have known each other for a long time," Fish said. "He's a huge tennis fan. He has a good game -- he's probably the best golfing tennis player. Put golf and tennis together, I think I've got him, though. And you can tell him I said that."
Garcia is expected back on Friday, when Fish will try to improve on a career record of 3-0 in ATP Masters 1000 semifinals. He has never won a title in the series, which ranks just below the Grand Slam level.