La Liga and Champions League holders Madrid have been linked with a move for Werner, though reports have suggested they are ready to pull the plug on a transfer because of an ear problem that forced him off due to dizziness in Leipzig's Champions League clash with Besiktas in September.
But Hasenhuttl said: "In winter nor in summer: We will keep Timo Werner with us. We are in intensive talks with his advisor."
Of the reports in the Spanish press of Madrid's interest, Hasenhuttl added: "These are things I do not take seriously."
Werner has a contract with Leipzig until 2020.