Forest have been in contact with Saelemaekers' representatives for over a year, even before his loan move to Roma last season.
The 25-year-old attacker spent the 2024/25 campaign on loan at Roma, where he overcame an injury-disrupted start to play 31 games, scoring 7 goals and providing 7 assists.
His versatile attacking abilities have caught the eye of Forest's manager Nuno Espirito Santo, who views Saelemaekers as a potential replacement and cover for Anthony Elanga, the winger currently linked with a move to Newcastle United.
AC Milan are asking for a fee in the region of 25 million euros, while Forest value the player slightly lower at around 20 million euros. This difference remains a key hurdle, but sources suggest it could be bridged depending on negotiations and Allegri's assessment.
Milan's new manager, Massimiliano Allegri, has paused all transfer discussions to evaluate Saelemaekers during pre-season before making a final decision on his future.
Meanwhile, Eintracht Frankfurt has recently emerged as a serious contender for the Belgian's signature.
Newcastle United previously sought information on Saelemaekers earlier this year but did not progress talks, as their interest shifted towards Elanga.
AC Milan have ramped up their pursuit of Bayer Leverkusen's midfield dynamo Granit Xhaka, with talks set to intensify in the coming days, according to reports from Sky Germany.
Nottingham Forest have reportedly renewed interest in signing Brentford and DR Congo striker Yoane Wissa during this transfer window.
Turkish giants Fenerbahce have reportedly launched an ambitious bid to sign Manchester City's veteran right-back Kyle Walker, offering the England international a two-year contract.
Atletico Madrid left-back Reinildo Mandava is set to depart the Spanish giants this summer, with his contract expiring at the end of July.
