The 24-year-old was one of the Magpies' star performers last campaign and has been attracting a lot of transfer interest ahead of the summer window. Lascelles was even voted as the club's Player of the Season.
Leicester City are now considering testing Newcastle's resolve, according to the Sun, who claim that a £35m offer is being prepared as the Foxes look to bolster their squad before the transfer window slams shut on August 9.
One reason for the club's interest in Lascelles is believed to be Manchester United's pursuit of their star defender, Harry Maguire.
The 25-year-old was seldom talked about in transfer speculation ahead of the World Cup this summer. However, Maguire's performances with the Three Lions has attracted a number of European football's biggest clubs.
It has been speculated that Manchester United have made the England international a top priority this summer, with recent reports suggesting that the Red Devils have already begun talks over the £65m move.
Newcastle star Lascelles is considered as a direct replacement for Maguire at the King Power Stadium, but talks with the Derby-born defender will have to reach an advanced stage before Leicester City allow their player to leave.
Manager Claude Puel has already seen four new players join his squad ahead of the new season, including Norwich City playmaker James Maddison and OGC Nice's Ricardo Pereira, for just under £60m - which has been recouped since the sale of Riyad Mahrez.
Leicester have also seen the likes of Bartosz Kapustka, Ahmed Musa and Nampalys Mendy return from loan spells away from the club.