The 30-year-old has also reportedly attracted interest from the New York Knicks and Atlanta Hawks ahead of free agency.
Hayward apparently declined his $34.2-million player option for 2020-21 on Thursday and is now an unrestricted free agent.
The Knicks and Hawks arguably pose the biggest threats to the Celtics and Pacers as each club has at least $40 million in cap space available this offseason, allowing them to sign Hayward outright.
Hayward is coming off his best season since joining the Celtics on a four-year, $128-million contract in 2017. He averaged 17.5 points, 6.7 boards, and 4.1 assists across 52 appearances during the 2019-20 campaign.