Germany international Havertz is one of Europe's most sought after talents having becoming a regular during the past four seasons - and was named in the Bundesliga Team of the Year last season.
The 20-year-old has already made 126 first team appearances for Leverkusen since his debut in 2016, and has also picked up seven full international caps.
According to Mundo Deportivo, the Reds have placed themselves at the front of the queue - ahead of the likes of Manchester United , Barcelona and Bayern Munich - for a summer transfer by making contact with Leverkusen representatives already.