The 22-year-old midfielder is out of contract with the Bundesliga outfit at the end of the season, and has previously expressed an interest in testing himself in the Premier League.
Reds boss Brendan Rodgers has been linked with a move for the boyhood Everton fan, as he looks to strengthen his Anfield ranks in January, but he is likely to face serious competition for Holtby's signature, with Inter Milan also reportedly monitoring the player's situation.
"We are talking with Schalke about a possible extension for another three years," his agent, Markus Noack, told calciomercato.com.
"Talks are going well at the moment but the situation has definitely changed in the last period because several offers from Spain and England came in."
Liverpool have been credited with an interest in several players during the upcoming transfer window, particularly in attack, as Rodgers aims to resolve his current shortage of strikers. However, he is also considering options in other areas with a view to the long-term future on Merseyside.
"Lewis is very good at Schalke but above all there is an English club which has made a very interesting proposal," Noack added. "My client will have to decide whether to continue to grow in Germany or to try a new experience at the end of this season.
"Inter Milan? We have not received any proposals from Italy and he would prefer [to play in] the Premier League and La Liga."