The Sunday Mirror reports that Roma are keen to sign Zouma to a permanent deal, but are prepared to settle for a loan deal.
Roma are keen to bring in Zouma as a replacement for Alessio Romagnoli, who joined AC Milan for £22million.
Reports claim Roma are prepared to sign Zouma on loan, if a permanent signing cannot be agreed.
The 20-year-old is currently third choice at Stamford Bridge and the Blues are also looking to land Everton ace John Stones before the transfer window closes.
Zouma joined Chelsea for just £12million in 2012.