The 27-year-old has fallen out of favour at Stamford Bridge since the arrival of Edouard Mendy, and Kepa has only managed eight Premier League outings across last season and this campaign so far.
Kepa is expected to feature for Thomas Tuchel's side more in January as Mendy is likely to be absent due to representing Senegal at the Africa Cup of Nations.
Sport Witness reports that more game time in January will not be enough to earn back the number one spot between the posts for the Blues, and a move to re-unite with former manager Maurizio Sarri is becoming increasingly favourable.
Lazio will reportedly not be able to complete a move for the goalkeeper in January due to financial reasons, but a loan deal in the summer is an option, if Chelsea can aid in paying a percentage of his wages.
Since arriving in West London in 2018, Kepa has played 113 games for Chelsea and kept 41 clean sheets during that time.