It is understood the clubs have made an agreement in principle that will allow the player to discuss personal terms and have a medical.
The fee for Havertz, who scored nine goals in 47 games for the Blues last season, could rise with add-ons.
Havertz, 24, joined Chelsea from Bayer Leverkusen in 2020 for a deal worth about £71m.
He also scored the winning goal for Chelsea in the 2021 Champions League final against Manchester City.
Havertz is set to move across London as Mikel Arteta looks to strengthen his Arsenal team following qualification for the Champions League.
Arsenal are also chasing England midfielder Declan Rice, the West Ham captain, but a second bid for the 24-year-old – worth up to £90m – was rejected on Tuesday.
Chelsea, meanwhile, are seeking to reduce their squad size and have also agreed a £30m deal with Manchester City for Croatia midfielder Mateo Kovacic, 29. Another midfielder, France international N’Golo Kante, 32, has agreed to sign for Saudi Arabian champions Al-Ittihad when his contract expires at the end of June.
The new ownership at Chelsea want to avoid letting players enter the final two years of their deals and Havertz, whose contract runs out in 2025, has not agreed an extension at the club.