Lenglet has emerged as a transfer target for Barcelona after quickly adjusting to life in Spain following a move away from Nancy in January 2017.
He swiftly claimed a first-team role under Jorge Sampaoli and continued to be depended upon by Eduardo Berizzo, Vincenzo Montella and Joaquin Caparros across the course of the recent campaign, missing just three games.
Still just 22, Lenglet made more LaLiga appearances than any other Sevilla player in 2017-18 and will be expected to be crucial again next term under Machin, if he stays put.
Former Girona coach Machin was announced as the full-time successor to Montella on Monday after Caparros' interim spell and he could yet secure the future of Lenglet despite Barca's interest.
"Lenglet is on vacation and will not decide [on his future] until he speaks with his new coach," the defender's agent Gregory Dakad told Estadio Deportivo .
"There is no news. The idea remains the same and we want to respect Sevilla."
Lenglet is likely to cost Barcelona around €35 million (£30.5m/$40.4m) should the transfer go through as Ernesto Valverde looks to bring in a long-term successor for Gerard Pique.