The Blues are reportedly on the hunt for attacking reinforcements with summer signing Radamel Falcao failing to live up to expectations.
And, according TyC Sports, Calleri is the man high on Jose Mourinho’s list to bolster Chelsea’s striking options.
The 22-year-old has been in impressive form for Boca this season, finding the net 20 times and laying on 11 assists.
The striker has previously been scouted by Arsenal, while Serie A side Inter Milan made an enquiry during the summer.
Boca are desperate to hold onto their star striker but are aware of growing interest in the forward from Europe.