The 22-year-old centre-back is expected to fly to England later on Saturday to undergo a medical, with a five-year contract in place should the move go through as planned.
The Athletic reported as far back as 22 July that Forest were in advanced talks with Sporting over a player who has attracted suitors from across Europe this summer, and negotiations have accelerated in recent days to bring the transfer to the brink of completion.
Reports in Portugal suggest the final package could rise to around €45m once bonuses are included, though the guaranteed fee is understood to be €40m.
Diomandé represented Ivory Coast at this summer's World Cup alongside Forest midfielder Ibrahim Sangaré, and has made 132 appearances for Sporting since joining from Danish club Midtjylland in January 2023 for a fee of around €7.5m, with add-ons that could have pushed the total as high as €12.5m.
He has won back-to-back Primeira Liga titles with the Portuguese club in 2023/24 and 2024/25, added the Taça de Portugal last season, and was part of the Ivory Coast squad that won the Africa Cup of Nations in 2023, also making 16 appearances for his country.
The move continues a busy summer of squad-building at the City Ground as new head coach Glasner, who previously pushed to sign Diomandé while managing Crystal Palace, looks to bounce back from a disappointing 16th-place finish last season.
Nottingham Forest have already completed the free signing of midfielder Xaver Schlager from RB Leipzig and paid Famalicão around €20m for attacking midfielder Gustavo Sá, while Sangaré and centre-back Murillo have signed new contracts, committing their futures to the club until 2029 and 2030 respectively.
For Sporting, Diomandé's departure would mark the club's fourth major transfer windfall of the summer, following the sales of Geovany Quenda to Chelsea, Morten Hjulmand to Atlético Madrid and Francisco Trincão to Al-Ahli.