The Blues have already splashed £230million in the current window to bring in the likes of Timo Werner, Hakim Ziyech, Ben Chilwell and Kai Havertz.
Malang Sarr and Thiago Silva also arrived at Stamford Bridge this summer on a free transfer.
Chelsea are also closing in on signing Rennes goalkeeper Edouard Mendy, with Chelsea boss Frank Lampard keen on providing competition for Kepa Arrizabalaga.
According to reports, Chelsea transfer chief Marina Granovskaia will finalise Chelsea’s summer spending by signing West Ham midfielder Declan Rice before the transfer window closes on October 5.
Lampard is a huge fan of the England international and is reportedly pushing for the signing of the midfielder despite Chelsea’s huge summer spending.
Rice was released from Chelsea’s academy aged 14 and Chelsea have two-and-a-half weeks to knock West Ham down from their £80m valuation and get a deal over the line.