The move should clear the way for Pierre-Emerick Aubameyang to join Arsenal, with Chelsea's Michy Batshuayi then going to Dortmund.
Chelsea and Arsenal have reportedly come to terms over a transfer fee for France international Olivier Giroud, per The Telegraph.
The Gunners are keen to sign Borussia Dortmund striker Pierre-Emerick Aubameyang this month after losing Alexis Sanchez to Manchester United, but the deal is thought to be hinged on whether or not BVB sign a replacement, with the German side having placed their crosshairs on Chelsea's Michy Batshuayi.
Chelsea's search for a brutish target man could soon come to an end, with several journalists reporting that the Blues have agreed an £18m fee for the French forward. They had pursued AS Roma hitman Edin Dzeko in recent weeks, but negotiations fell through after they refused to meet his wage demands, as well as his contract length request.
Giroud, on the other hand, does represent good short-term business for Chelsea at that price. He is a potent scorer with years of Premier League experience and despite his age, can still compete at the highest level.
The 31-year-old has been at the Emirates since 2012 and has scored 105 goals, along with 41 assists, in 252 appearances for the Gunners.
Arsenal were intent on avoiding more business with a Premier League competitor in this window and would have much preferred to move him to Dortmund, but the striker's desire to remain in London has seen the Blues come close to an unlikely signing.
Batshuayi is now expected to join the German side on loan, but with Arsenal set to play on Tuesday and Chelsea also in action on Wednesday, it could make things difficult, especially for the Blues, who are without the injured Alvaro Morata.