Lenglet has impressed at the Ramon Sanchez Pizjuan since signing from Nancy in January 2017, leading to rumours that La Liga title favourites Barca could be set to make a move for the centre-back.
The 22-year-old has previously insisted he is happy at Sevilla and senior club officials are clear in their intent to keep the Frenchman.
"We are working on [Clement's future] and on some other players," said Castro, as reported by Sport. "These are internal conversations and we hope that they will end well.
"We have no record of any interest in him."
Lenglet has made 27 La Liga appearances this season, scoring three goals, with Sevilla in sixth place and facing Barca this weekend.
Sevilla will face Bayern Munich in the Champions League quarters, with the first leg taking place on April 3.