The 33-year-old was believed to have been one of the top candidates for the job thanks to his work in North London, where he has twice filled in as Tottenham interim head coach.
Mason and Anderlecht - whose captain is ex-Tottenham defender Jan Vertonghen - were said to have been engaged in talks for the Englishman to take over from Brian Riemer, who was sacked last month.
However, according to the Evening Standard, Mason will now be staying at Tottenham - where he is under contract until the end of the 2026-27 campaign - rather than joining Anderlecht.
The news will come as a significant boost to head coach Ange Postecoglou, who lost former assistant Chris Davies to Birmingham City over the summer but will keep his current crop of coaches together for the time being.
Why has Mason chosen to stay at Tottenham?
The decision for Mason to remain at Tottenham was reportedly a mutual one, as both the 33-year-old and Anderlecht decided that now was not the right time for him to jump into a head coach role.
Mason is understood to be happy working with head coach Postecoglou, who employed him as part of his backroom team after the Englishman ended the 2022-23 season as Spurs' interim manager.
Mason temporarily replaced Cristian Stellini at the helm following the Italian's disastrous reign in the wake of Antonio Conte's exit, prior to which he also oversaw seven games at the end of the 2020-21 season.
By stepping into Jose Mourinho's shoes that year, Mason became the youngest temporary or permanent Premier League head coach in history at just 29 years old, and he also managed Tottenham in the 2020-21 EFL Cup final, which they lost 1-0 to Manchester City.
Mason made 70 appearances for Tottenham after graduating from their youth system, scoring four goals, but his playing career was cut short by a serious head injury in 2018 while at Hull City.
How big a boost is Mason's decision to stay?
An incredibly respected figure in North London, Mason is regarded as a fundamental part of Postecoglou's coaching setup and was equally highly-rated by Conte, whom he worked for as a technical coach.
The former midfielder choosing to stay means that Postecoglou does not have to work around two major backroom staff exits in a matter of months, and with Mason being a young coach with experience of coming through the Tottenham ranks, his advice to academy players will be invaluable.
Stability is hugely important to Tottenham at a time where their previous frailties have started to rear their ugly heads again, having thrown away a 2-0 lead to lose 3-2 to Brighton & Hove Albion last weekend.
That collapse leaves Spurs ninth in the Premier League table with 10 points from their opening seven matches, and the Lilywhites are next in action at home to London rivals West Ham United on October 19.