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The Wales international, 29, has enjoyed a renaissance under Conte on the left of Spurs' back three and last season started 34 of 36 matches after the Italian's arrival, including 26 of 27 in the Premier League.
Davies, who is going into his ninth season at the club, faces competition this term from Clement Lenglet, who has joined on loan for the season from Barcelona and was one of five summer signings to make his debut in Saturday's friendly win over Rangers, along with Ivan Perisic, Djed Spence, Yves Bissouma and Fraser Forster.
Spurs would enter the market for another new centre-back if both Japhet Tanganga and Joe Rodon leave the club this summer.
Tanganga is attracting interest from AC Milan and Davies’ Wales team-mate Rodon desperate for first-team football before the World Cup in November.