The defender was signed from Boca Juniors before being loaned back for this season.
However, such has been his form that Anselmino is now being considered as a January addition by Blues management, says Bolavip.
Chelsea splashed out €18m for Anselimo over the summer.
It's also been revealed Enzo Fernandez sent Anselimo a message through Whatsapp after the deal was struck.
"I congratulate you on this step," Fernandez's message read. "Now, smash it in the time that you have left at Boca and I'll wait for you. You'll smash it here too. Count on me for whatever you need."
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