The proposal, structured as a £20m initial fee plus £2m in add-ons, is now under consideration at Selhurst Park. Muñoz thrived under Glasner's back-three system during the Austrian's two and a half years in south London, helping Crystal Palace to the FA Cup, Community Shield and Europa Conference League before his former manager left for the City Ground this summer.
The 30-year-old Colombia international has two years left to run on the contract extension he signed in April last year, giving Palace no obligation to sell if the numbers don't meet their valuation.
Nottingham Forest have widened their search for a right wing-back rather than relying solely on the Muñoz pursuit, having also held talks over Celta Vigo's Javi Rueda in recent days.
Ola Aina has started in the role in both of Forest's opening two matches of the season, a pair of home defeats to Leeds United that have added urgency to Glasner's efforts to reshape the position before the transfer window closes.
Muñoz joined Palace from Genk for £6.9m in January 2024 and went on to make 108 appearances, scoring 11 goals and contributing significantly to the club's most successful period in its history.
Everton and Tottenham have also been credited with interest in the Colombian this summer, though Palace manager Pierre Sage has consistently maintained that Muñoz remains part of his plans, starting him in the club's opening-day defeat at Everton.
Whether that stance survives a concrete offer of this size, with days left before the deadline, may prove the deciding factor in whether Glasner gets his man.