According to the Mirror's Darren Lewis, the two sides are among several eyeing the Spaniard, who has made just four appearances for the Blues since Maurizio Sarri took charge in the summer.
Fabregas is in the final year of his contract at Stamford Bridge and can negotiate with foreign clubs regarding a free transfer next summer from January.
If the Blues opt not to give him a new deal, the winter transfer window will be their last opportunity to recoup a fee for him.
The 31-year-old has not made a single appearance in the Premier League this season, though that is partially because of a knee injury that kept him out of action at the start of the campaign. Fabregas has made the bench in Chelsea's last three outings but remained an unused substitute.
Fabregas has nevertheless enjoyed working under Sarri and recently expressed his desire to remain with Chelsea:
Sky Sports Premier League @SkySportsPL
"I still have a lot of football left in me!" 📝 @ChelseaFC midfielder Cesc Fabregas says there has been no contract offer from the club, but he would love to continue playing under Maurizio Sarri! 🔵 Watch Chelsea take on Southampton live on Super Sunday from 11am! https://t.co/Ro8hntu3sr
The Spaniard isn't especially mobile but he can unlock a defence thanks to his tremendous vision and the passing range to match.
He showcased a little of what he can do against Vidi in the UEFA Europa League earlier this month:
Fabregas is flexible enough to perform multiple roles in midfield, too—he can dictate the tempo as a deep-lying playmaker or play in a more advanced role as he did with Barcelona.
It seems he'll be used in the former as a deputy to Jorginho this season, per Goal's Nizaar Kinsella:
He still has plenty to offer the Blues, and it's little wonder he'll have plenty of suitors having racked up 122 goals and 201 assists in his club career.
Atletico don't tend to score a lot of goals—they've only found the net nine times in eight La Liga matches this season—so they could benefit from his creative spark, and he could be a bargain signing in January if Chelsea don't tie him down.