Hayward's agent, Mark Bartelstein, however, told ESPN's Adrian Wojnarowski that his client "hasn't made a decision yet. We are still working through it."
Jazz president Steven Starks tweeted that he trusts Bartelstein's word that no decision has been made.
We trust Gordon and his agent that no decision has been made. Good communication all day and a great relationship.— Steve Starks (@StevenStarks) July 4, 2017
Bartelstein also told the Boston Globe that although Hayward initially planned to announce his decision Tuesday, he was unsure if that would still be the case.
"That was the goal, but now we've got to kind of regroup here a bit," he told the Globe.
In Boston, Hayward would be reunited with Brad Stevens, who also coached him in college at Butler.
Hayward's decision would mark the second consecutive Fourth of July that a high-profile free agent would switch teams in free agency. Last year, Kevin Durant announced that he was leaving the Oklahoma City Thunder for the Golden State Warriors.
It also would mark the second straight summer that the Celtics have successfully recruited a coveted player on the free-agent market. Last year, Al Horford signed with Boston.
Boston would now need a series of transactions to create cap space for Gordon Hayward. The Celtics would have to pull the qualifying offer on Kelly Olynyk, renounce free agents Jonas Jerebko, James Young, Gerald Green and waive the contracts of Jordan Mickey and Demetrius Jackson (or trade). The Celtics would be left with $27.6M in room and likely need to move the contract of Terry Rozier or Marcus Smart. Trading Rozier would have the Celtics short $1M of a max salary a lot.
A contingent from the Jazz, including the recently acquired Ricky Rubio, met with Hayward on Monday in a 3½-hour meeting at Hayward's San Diego home. Rubio, who was acquired as a key part of the Jazz's plan to re-sign Hayward, traveled from Spain for the meeting.
The All-Star swingman, who also met with the Heat on Saturday and Celtics on Sunday, will command a maximum salary after opting out of the final season of his contract.
Hayward, 27, has steadily developed into a franchise-caliber player since the Jazz selected him with the ninth overall pick of the 2010 draft. He has improved his scoring average each year, topping out at 21.9 points per game last season, when Hayward made his first All-Star appearance and led 51-31 Utah to its first playoff appearance since 2012.
The last Utah player to be selected to an All-Star Game was Deron Williams in 2011.
Hayward also averaged a career high in rebounds (5.4 per game) last season, dished out 3.5 assists per game and shot 47.1 percent from the floor, his highest mark since his rookie season, when he had a limited role.
Hayward, whose only previous playoff experience consisted of a sweep at the hands of the San Antonio Spurs in a 2012 series in which he was 6-of-33 from the floor, starred in his second appearance on the postseason stage. He averaged 24.1 points, 6.1 rebounds and 3.4 assists in the playoffs -- numbers skewed low because food poisoning limited him to nine ineffective minutes in Game 4 against the Los Angeles Clippers -- to help the Jazz advance to the second round for the first time since 2010.
Hayward's 8,077 career points rank eighth in Jazz history. He has career averages of 15.7 points, 4.2 rebounds and 3.4 assists per game.
Hayward was ranked No. 6 on the list of top available free agents this offseason compiled by ESPN's Kevin Pelton.
ESPN's Tim MacMahon contributed to this report.