Glasner, who replaced Vitor Pereira at the City Ground, is already working on other additions this summer, with midfielder Xaver Schlager set to sign and a second bid expected for Tottenham's Lucas Bergvall.
Central defence has emerged as another area in need of reinforcement, with Nottingham Forest relatively light in that department as Murillo continues his return from injury and interest persists in Jair Cunha.
According to Record, the 22-year-old Ivory Coast international is expected to leave Sporting this summer, having joined the club from FC Midtjylland in 2023 and been linked with a big-money Premier League move ever since.
The Portuguese newspaper reports that Sporting are demanding a fee of €50m (£42.4m) for the defender, with Newcastle United, Crystal Palace and Leeds United also mentioned as possible destinations. AC Milan are reportedly among the European clubs weighing up a move too, with Ruben Amorim having previously worked alongside the young centre-back.
Record adds that discussions have already taken place between the two clubs over a potential deal, with Diomande, currently still on his summer holiday before returning for pre-season training, considered a top target for Forest this year. No official offer has been made as yet.
Murillo's continued recovery remains a factor in Forest's defensive planning after the Brazilian missed the weekend's win over Notts County. Glasner offered an encouraging update on his situation.
"He is already training and doing good rehab sessions, but now it is increasing the intensity and getting him back to normal training," the Forest boss said.
Diomande would represent a significant statement of intent for Forest if a deal could be reached, given the level of competition already circling the defender and the fee involved.
Glasner's familiarity with the player from his time at Crystal Palace, where the Ivorian was previously said to have been a target, could work in Forest's favour as talks continue, though Sporting's asking price means any deal is likely to require considerable investment before it can be completed.