Earlier on Wednesday, tournament director Jamie Baker said he informed Osaka's team that organisers were "completely open for any discussions" in case of any issues.
"Staging The Championships in 2021 is our number one priority and we are actively engaged in scenario planning in order to deliver on that priority," AELTC Chief Executive Sally Bolton said in a statement.
The Indian Davis Cupper beat British Jamie Baker 7-5, 6-2 in the first round of the Lexington Challenger.