The 6-foot-10, 260-pound Baynes averaged 4.9 points, 4.4 rebounds and 15.5 minutes per game last season with the Detroit Pistons.
Baynes' strength is defensive rebounding, and that is where Boston needs help.
The Celtics cannot sign the 30-year-old Baynes officially until Gordon Hayward is officially signed to a maximum-contract salary that will pay him $29.7 million next season.
Baynes tweeted a hint as to where he will sign: "Does anybody know if there's good BBQ in Boston? Asking for a friend."