The former Tottenham fullback is being linked with Chelsea.
But Saints boss Hasenhuttl remains unmoved by any speculation: "Before we go now through every player who maybe has interest from someone else, we should maybe concentrate on the games ahead.
"The transfer window is now open still for a long time, and this is something that will definitely affect your questions in the future.
"But for me it's more important to bring the players into the shape to compete in the Premier League, and this is the focus I have."
Asked about a possible loan deal for Werner, Hasenhuttl replied: "Nice try!
"But as I said before, I'm not here today to speak about other players.
"We know there are some good players out there.
"We have our eyes open, the transfer market is open for another 30 days or something.
"That's too long definitely; we have done well so far, but it doesn't mean we don't want to do well again in other positions too."