Southampton boss Mauricio Pellegrino again left Virgil van Dijk out of his squad for their draw with Huddersfield.
But Pellegrino has remained tight-lipped on a possible January move to Liverpool or Manchester City.
He said: "I decided that was best for this moment. This is the reason. I am responsible for picking 11 players, and I intend to pick the best for the team.
"Around him will be a lot of speculation and we have to wait to see what happens.
"Van Dijk's future? I don't know, we'll have to wait, but I will repeat, there will be a lot of speculation around him. We have to wait."