The 34-year-old French international is expected to sign a two-year deal with the Serie A side and could complete the move by the end of the week.
Giroud joined Chelsea from Arsenal for £18m in January 2018 and last month extended his contract until 2022.
Chelsea would be able to command a transfer fee for the forward, who last season scored 11 goals in 31 appearances.
After the signings of German forwards Kai Havertz and Timo Werner last summer, Giroud made only eight Premier League starts in the 2020-21 season.
Giroud has scored 39 goals in 119 appearances for the Blues, winning the Champions League, Europa League and FA Cup.
The World Cup winner, who also won three FA Cups with Arsenal, came off the bench in France’s Euro 2020 defeat against Switzerland in the last-16.