The 23-year-old was subject to late interest in the summer window from the West Londoners, who allegedly failed with a £43m offer.
The Blues are thought to be keeping tabs on Alvarez’s situation and a recent report suggests that they are preparing to reignite their interest at the midway point of the campaign.
However, Sport claims that Chelsea could face stiff competition from the La Liga giants Barcelona for the midfielder’s signature.
The Catalan giants are understood to have sent scouts to watch the Mexican in the Champions League group stage against Liverpool, Napoli and Rangers this season.
The report outlines that the Blaugrana have identified Alvarez as a possible replacement for Sergio Busquets, who has a deal until 2023.
Busquets, 34, now faces an uncertain future at Camp Nou and has been linked with a potential switch to Major League Soccer.
Barcelona have also been credited with an interest in Wolverhampton Wanderers’s Ruben Neves, Real Sociedad’s Martin Zubimendi, PSV Eindhoven’s Ibrahim Sangare and Benfica’s Enzo Fernandez.