The Magpies have been locked in negotiations with the LaLiga outfit for some time over the 26-year-old Frenchman, who has an £8.7million release clause in his contract.
However, sources on Tyneside have indicated that they are close to reaching an agreement which would hand manager Rafael Benitez his first summer signing.
Former Auxerre and Villarreal central defender Lejeune signed for Manchester City in July 2015, but was loaned straight out to Spanish second division side Girona, where he had spent the previous campaign, also on loan.
He joined Eibar on a permanent deal for just £1.2million 12 months later and made 34 league appearances last season as the club finished in 10th place.
It has been a testing few weeks for the Magpies in the summer transfer market with Benitez still awaiting a breakthrough.
Newcastle remain hopeful of clinching a loan deal for Chelsea forward Tammy Abraham, who is currently on England Under-21s duty in Poland, although they could face competition from both Brighton and Swansea, with the Welsh club having gone public with their interest.
Meanwhile, goalkeeper Matz Sels, who joined the Magpies in a £5million switch from Gent last summer, is set to leave on loan with Belgian side Anderlecht close to agreeing a move.
Source : PA
Source: PA