The 24-year-old made his Chelsea debut in 2021 and has since featured 63 times for the West Londoners, scoring four goals over that two-year period.
Chalobah has been around the club's first team for the past two seasons, managing to appear in 25 Premier League matches in the 2022-23 campaign.
Despite failing to earn a cap for the England senior side to date, the centre-back has been involved with his nation at Under-20 and Under-21 level in the past.
According to the Daily Mail, Nottingham Forest have submitted a last-minute bid for Chalobah in this summer's transfer window, with Steve Cooper looking to bolster his defensive options.
The report claims that the East Midlands club have offered Chelsea £25m for the 24-year-old, who also has interest arriving from outside of England.
It is understood that Bayern Munich are keen on bringing Chalobah to the Bundesliga this season, with the German champions hoping to regain the league crown this term.
Former Blues boss Thomas Tuchel is currently at the helm at the Allianz Arena, and it is believed that the German would like to reunite with the defender before the window closes.
Chalobah's ability to operate in a number of positions across the backline is said to be a significant factor in Bayern's fondness of the player.
A separate report is claiming that the Bavarians are also in the hunt for Manchester City right-back Joao Cancelo, with Tuchel's men hoping to recruit the Portuguese on a temporary deal for the 2023-24 season.
The former Juventus man secured a loan switch to Bayern for the second half of last season, featuring in 15 league games as they narrowly pipped Borussia Dortmund to the Bundesliga title.
Despite an influx of players since their promotion to the Premier League in 2022, Nottingham Forest are still starting the likes of Scott McKenna and Joe Worrall - players who were regulars for the club in the Championship.
Chalobah could become the second defensive incoming of deadline day for the Tricky Trees, with Nuno Tavares's loan move from Arsenal being confirmed earlier on Friday.
The left-back spent last term at Marseille in Ligue 1 as he searched for game time away from the Emirates, starting 23 league matches and scoring six goals in the process.