According to NBC Sports Boston's A. Sherrod Blakely, the two sides are "close" to a deal with the start of the regular season less than a month away.
Hayward has been part of the Nike family for the majority of his pro career, but he entered the summer as a sneaker free agent.
The 28-year-old garnered interest from several of Nike's competitors, and according to ESPN.com's Nick DePaula, New Balance and Anta both pitched Hayward on entering the fold as a brand ambassador before he went back to the Swoosh.
Hayward—who signed a four-year, $128 million deal with the Celtics last summer—fractured his ankle in the Celtics' 2017-18 season opener and was ruled out for the remainder of the season.
The one-time All-Star was recently cleared for five-on-five work and is on track to make his 2018-19 debut on schedule.
"Like anything, there's always going to be a period of adjustment," head coach Brad Stevens said, according to The Athletic's Jay King. "From my eye and anybody else that may have watched him work out, he looks like he's looked before."
The Celtics will open their regular season Oct. 16 at home against the Philadelphia 76ers.