Pereira was Nottingham Forest's fourth manager of last season and helped keep the club in the Premier League, but reports suggest he could now be replaced by former Crystal Palace boss Glasner.
The prospective move has reportedly frustrated officials at Selhurst Park, given the recent history between the two clubs.
Pereira had been expected to hold talks over a new contract after helping retain Forest's top-flight status, but has instead confirmed his departure, with Glasner understood to be in a strong position to take over.
Any move for Glasner is unlikely to be well received by Palace supporters, with little love lost between the two clubs after Forest replaced Palace in last season's Europa League.
UEFA ruled that American businessman John Textor's influence over both Palace and French club Lyon meant the two sides could not compete in the same European competition.
Palace were demoted to the Conference League as a result, a decision that worked in Forest's favour.
Glasner was also a strong candidate to take over at the City Ground in December 2023 when Steve Cooper departed, though the club opted for Nuno Espirito Santo on that occasion.
One source has suggested that Forest were prepared to sack Pereira if Glasner indicated any willingness to move to the Midlands club, and the Austrian is currently without a job having left Crystal Palace at the end of last season.
Glasner delivered considerable success during his time at Selhurst Park, leading Palace to the FA Cup in 2025 and the Conference League in 2026.
By the time Palace lifted their first European trophy, it was already known that the campaign would be Glasner's last at the club.
The Austrian's achievements at Selhurst Park mean he leaves with his reputation significantly enhanced, making him an attractive option for a Forest club looking to build on last season's Premier League survival.
Glasner's earlier interest in the City Ground role back in December 2023 suggests a familiarity with Forest that could work in his favour, should talks progress further this time around.