Virgil Van Dijk is absent from the Southampton squad for their pre-season friendly with Brentford.
The Saints defender, who had been linked with a move to Liverpool earlier this summer, has been training alone after expressing his desire to leave.
The Reds insisted they had ended their interest but Mauricio Pellegrino revealed that he is not keen to feature for the Saints.
"He is not involved with the team because psychologically he is not 100%," Pellegrino said.
Speaking to BBC Radio Solent, the Argentine added: "When I was talking with him, the boy said that he is not available to play because he wants to leave.
"I need to work with a player that works at 100% to defend Southampton.
"This is the decision. I had to say: 'OK, if you don't want to be involved because you don't feel OK, you have to train alone until this period of time.'"
Southampton: Fraser Forster, Jeremy Pied, Jan Bednarek, Maya Yoshida, Matt Targett, Steven Davis, Oriol Romeu, Shane Long, Dusan Tadic, Sofiane Boufal, Charlie Austin.
Substitutes: Gazzaniga, Taylor, Gradds, McQueen, Gallagher, Jones, Gabbiadini, Bertrand, Hojbjerg, Stephens, Wood, Johnson.