Southampton captain Virgil van Dijk has not been included in their squad for a training camp in France this week.
The defender, 26, has been strongly linked with a move to Liverpool, although the Anfield club said they ended their interest last month.
Southampton say they do not want to sell the Netherlands international.
Saints boss Mauricio Pellegrino said last week that Van Dijk had been training alone because he feels the player is "not 100%" mentally.
Van Dijk, who joined Southampton in 2015 from Celtic, travelled with his team-mates for a pre-season tour in Austria earlier this month but has been left out of Pellegrino's 25-man squad heading to France.
Southampton will play Saint Etienne in a friendly on Saturday as they prepare for their Premier League opener at home to Swansea City on 12 August.