The 20-year-old is one of the hottest prospects in German football and is widely tipped for a move away from the Bundesliga side.
Chelsea, Manchester United, Liverpool and Manchester City are among the clubs interested in securing his signature, according to Bild.
But the English quartet will face competition from Bayern Munich, Barcelona and Real Madrid.
All seven clubs are said to have contacted the player’s agent about a potential move, although Havertz is valued at a whopping £110 million.
A January switch could be possible, but the midfielder would prefer to stay put at Leverkusen until the summer in a bid to nail down a place in Joachim Low’s Germany squad for Euro 2020.
Last summer Bayern attempted to prise the youngster away from their domestic rivals, but had a £76 million bid turned down.
Havertz is said to be likely to make a decision on his future in the next few weeks as he considers which club – and coach – would best suit him.
He suggested in an interview with Marca that a move abroad could be on the cards.
“I think I've picked up enough international experience at Leverkusen,” he said.
“I know the rhythm of these international matches and I'm confident that I can go abroad at any moment and play at clubs outside of Germany.
“For the moment, I want to have a good season. Afterwards, we'll see.”
Havertz has scored three goals in 16 appearances in all competitions for Leverkusen this season.
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