Giroud, 33, has found first-team chances limited under Frank Lampard this season, following the emergence of Tammy Abraham as the first-choice striker.
Now according to Football.London both Inter and Atletico have stepped up their pursuit of the former Arsenal man.
Atletico attempted to sign Giroud on loan in the summer of 2018 and are keen to add more firepower to their strikeforce that has netted just 16 goals in 16 La Liga games this season.
Chelsea manager Frank Lampard, meanwhile, is relaxed about the upcoming January transfer window after his side reached the Champions League knock-out stages with a 2-1 win over Lille.
Goals from Tammy Abraham and Cesar Azpilicueta goals, sent the Blues through as runners-up to Valencia.
By then Chelsea could have reinforcements now they are able to sign players again in January after the club’s transfer ban was lifted.
“I’m calm about this window. I know what the squad is. We feel very together in the dressing room,” Lampard said.
“We are improving and even the little bumps during the last two weeks are part of the process and we don’t see so much in January that you can do great business.
“If it is there to be done and it feels like it is right for the club that is a conversation for me and upstairs, but I am very calm with January.
“I believe in what we’ve got now and I don’t think we will be crazy just because the transfer ban has been lifted. I think we just need to keep working.”
11 BUSINESS NUGGETS FROM SUPER EAGLES BRONZE MEDAL TRIUMPH. The content of this ebook will propel you above your competition. DOWNLOAD NOW!!!