However, ahead of Saturday's game against Schalke, Hasenhuttl has insisted the 22-year-old will remain in the Bundesliga until the summer. German daily Bild report the Reds are prepared to pay 15 million euros extra to sign Keita this month.
Liverpool FC fans have been dreading this day since last summer, when the Coutinho saga began.
Klopp said: "My understanding is there is nothing to say".More news: No Traveling for New York's Columbus Statue, Mayor Decides
Sporting director Michael Edwards will negotiate with Ralf Ragnick about bringing forward a deal for Naby Keita this month.
Want news and features on the Reds on your Facebook timeline? And they have shored up their suspect defence by paying an eye-watering 75 million ($102 million, 84 million euros) to Southampton for defender Virgil Van Dijk.
Liverpool must do all they can so seal a January move for their incoming purchase - whether they succeed or fail in that respect could end up being a season-defining moment.
Furthermore, his versatility means that he can comfortably change positions with wingers and attacking midfielders, confusing the opposition defence as they can never be sure who is playing in which position.More news: David Silva Tipped To Return As Manchester City Face Liverpool Test
Liverpool have also been linked with Monaco ace Thomas Lemar and Leicester winger Riyad Mahrez.
While bringing in any of those names would add great quality to this Reds outfit, it is Keita who has to be the primary focus for the time being.
According to the Sky Italia journalist, the Egyptian has been identified by the European champions as a potential "Galactico" signing - concerning news for Liverpool supporters.More news: Has $70.42 Million Position in Nike Inc (NKE)