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According to the Evening Standard, the Belgium international has been a key figure in a transfer triangle involving the Blues, Dortmund and the Gunners. The Bundesliga club will only sanction Pierre-Emerick Aubameyang's transfer to the Emirates if they can sign a replacement.
Batshuayi will replace the Gabon international at the Signal Iduna Park until the end of the season. The two clubs have reached an agreement over the terms of the loan deal and personal terms with the 24-year-old have already been agreed.
The German outfit were also looking at the option of signing Giroud as part of the Aubameyang deal. However, the France international turned down the opportunity to join Dortmund as he wants to continue in London.
This has allowed the Premier League winners to make an approach for Giroud as they are looking to bring in a striker to provide competition for Alvaro Morata. Chelsea had earlier identified Edin Dzeko as a target, but a failure to agree terms with the AS Roma star saw the move falling through.
Chelsea then shifted their focus to signing Giroud and he will replace Batshuayi as the second striker at Stamford Bridge. Antonio Conte was keen on strengthening his side's attack after the Spain international struggled in the last few months.
The Arsenal striker has already agreed personal terms with the west London club after the Gunners and Chelsea settled for a fee of around £18m ($25.5m), reports the Telegraph. Giroud will undergo his medical on deadline day of the mid-season transfer window.
Giroud's move to Chelsea will have a domino effect that will then see the Blues sanction Batshuayi's loan move to Dortmund. This in turn will see Peter Stoger's side allowing Aubameyang to join Arsenal.
Arsenal suffered a 3-1 defeat at the hands of Swansea City at the Liberty Stadium on 30 January. Arsene Wenger said his compatriot could join Chelsea, while stressing that he should find out the outcome of the Aubameyang deal on Wednesday.
"We will know about [Aubameyang] tomorrow morning. It's a possibility [that Giroud will join Chelsea], but all that will be decided tomorrow morning. We will inform you once that is more definite," Wenger told Sky Sports.
Chelsea have already completed the signing of AS Roma defender Emerson Palmieri for £17.5m on Tuesday. The Blues will complete two more deals, which will see Giroud move to Stamford Bridge and Batshuayi join Dortmund on loan on deadline day.