The Spaniard has struggled for regular game time at Chelsea, with Edouard Mendy being first choice between the sticks under Thomas Tuchel.
Kepa has been linked with moves away from Stamford Bridge in recent transfer windows but a transfer is yet to materialise.
The Blues star has drawn admiring glances from Newcastle United, who are looking at the possibility of signing him this summer, while Serie A giants Lazio are also credited with interest.
And according to Italian daily Il Messaggero, Kepa is willing to forgo part of his €5m wages to leave Chelsea and move to Lazio in the upcoming window.
However, despite Kepa being a player Lazio coach Maurizio Sarri admires, he is not their priority shot-stopper target this summer
Lazio have zeroed in on Atalanta custodian Marco Carnesecchi as their top target to bolster their goalkeeping department, while Kepa remains on their radar.
It remains to be seen whether Lazio will make any concrete moves for the Chelsea star in the upcoming window.