If athletes from those countries did compete, ASB could remove its branding and replace it with signage expressing support for Ukraine and the bank's opposition to the Russian invasion.
ASB would become the first naming-rights sponsor of an ATP and WTA event to pull its branding because of the presence of Russian and Belarusian players in the field.
In a joint statement realeased by ASB, Tennis Auckland and Tennis New Zealand, the bank confirmed their financial support for the tournament would remain.
"Media reports this week have speculated about the involvement of Russian or Belarusian players in the January 2023 event," the statement read. "To be clear, the 2023 tournament will go ahead as planned with ASB's full financial support.
"Under Women's Tennis Association (WTA) and Association of Tennis Professionals (ATP) regulations tournament organisers must allow Russian and Belarusian players to enter the tournament if they are sufficiently well ranked.
"We all understand that Tennis Auckland and Tennis New Zealand are in a difficult position and there is no suggestion that ASB would withdraw its significant financial support for the tournament should Russian or Belarusian players compete."
The statement added: "ASB has long been a passionate supporter of tennis in New Zealand. This year the bank celebrated its 25th year sponsoring the ASB Classic tournament in Auckland by announcing it has signed as the naming rights sponsor for a further three years.
"We all love tennis and look forward to this great annual event being back after a two-year Covid hiatus. The ASB Classic is one of the highlights of the summer calendar, particularly in Auckland, and is expected to bring around $27 million in much needed additional consumer spending to the Auckland region."
In July, Wimbledon banned those players, prompting a backlash from the Tours who stripped the Grand Slam of ranking points.
Tournament entries for the women's Classic close on 21 November and for the men's tournament a week later.