Sarri himself has also been linked with the Roma job after a mixed season brought criticism from fans, with suggestions Frank Lampard could take over at Stamford Bridge if the Italian departs.
With Massimiliano Allegri leaving the Italian giants last week, Pochettino and Sarri have emerged as the main contenders for the role, according to Gazzetta dello Sport.
But no decision will be made until after the European finals.
Allegri left the club having won 11 trophies in five years, winning a quintuple of league titles in that time.