A number of clubs have been linked with the defender, who was outstanding last season on the club's return to the Premier League.
Chelsea, Liverpool and Everton have also been credited with an interest in the 24-year-old, who succeeded Fabricio Coloccini has captain at St James's Park two years ago.
Lascelles, for his part, isn't looking to leave the club he joined in 2014.
The former England Under-21 international, under contract until 2023, reiterated his commitment to United in an interview with the Gazette last month.
Lascelles said: “This is the happiest I’ve been. I’m playing week in, week out, and I’m the captain here. The fans love me. I’ve got a good relationship with them, and we’re doing well, too.
“I’m very happy here. I need to be playing football at a good club – and that’s what this is.”
But would Rafa Benitez – who is yet to agree a transfer budget with owner Mike Ashley – consider selling Lascelles?
Newcastle's manager was asked if he would sell Lascelles ahead of the final game of the season against Chelsea. last month.
Benitez insisted he didn't want to sell Lascelles, though he qualified his answer.
“Not really," said Benitez. “If you want to continue growing, normally you have to try to keep your best players.
“Jamaal has a great potential, but if you cannot compete, or you cannot keep the level of your team, then maybe you have to sell one player to be sure that you can bring in other players.
“When people say ‘wheel and deal’ – sometimes you have to do it, because if not, you don’t have the money.
“If you don’t have the money, the main thing is to be sure that if you sell this one for Â£40million, you have two at Â£20million who can do well. Then you can be better.”
The Evening Standard claim that Tottenham are lining up Lascelles as a potential replacement for Toby Alderweireld, who has rejected the offer of a new contract at White Hart Lane.