RB Leipzig forward Werner, who was linked to the Reds last week, seems set to stay at his current club for at least another season while Borussia Dortmund are leading the race for Dahoud's signature.
Werner addressed the rumours of interest from English clubs after Leipzig's shock 3-0 loss to Werder Bremen, saying he is happy with the Bundesliga club.
"I want to keep growing together with RB Leipzig and keep developing here," he told Welt am Sonntag. "I am still only 21 years old and still have plenty of years ahead of me.
"I am very happy at Leipzig. Joining this club has been a stroke of luck. I have found my way again under [coach] Ralph Hasenhuttl."
A report in Kicker has also claimed that Dortmund are the most likely destination for Dahoud in the summer, with a decision on his future due before the end of April.
The 21-year-old midfielder, also linked to Manchester City recently, could be available for £10-£12million because of a release clause in his contract at Borussia Monchengladbach.