Following a productive loan spell with PSV Eindhoven, with whom he scored four goals in 36 games and won the KNVB-Beker, Branthwaite has enjoyed a breakout season in the Toffees backline.
The 6ft 4in centre-back has ousted Ben Godfrey and Michael Keane to become James Tarkowski's first-choice partner, starting each of his side's last 13 Premier League games and keeping four clean sheets in the process.
The 21-year-old has been with the club since 2020 - joining from Carlisle United - and has one goal to show from 28 matches, while he was also a part of England Under-21s' Euro 2023 winning squad this summer.
Despite Everton's unprecedented 10-point deduction for breaching the Premier League's Profit and Sustainability rules, Sean Dyche's side are hovering just above the relegation zone, thanks in no small part to Branthwaite's efforts.
Back in October, the defender extended his contract with the Premier League ever-presents until the summer of 2027, but the Toffees would be fighting an uphill battle to keep hold of him if they are demoted to the Championship.
Both Man United and Tottenham have been credited with an interest in Branthwaite, and the two Champions League chasers have been tipped to make a move for his signature as early as January.
However, Football Insider claims that Everton will not entertain any winter approaches for Branthwaite, whom they view as a pivotal asset in their fight against relegation.
Branthwaite is believed to be aware of the "concrete" interest in his services, but Everton are confident that they can keep Man United and Tottenham at arm's length next month.
As a result, the two Big Six sides will have to prioritise other defensive targets next month, as Tottenham endeavour to find cover for the injured Ashley Phillips, Eric Dier and Micky van de Ven.
Having sold Davinson Sanchez to Galatasaray over the summer, as well as loaning out Joe Rodon and Japhet Tanganga to Leeds United and Augsburg respectively, Cristian Romero is Ange Postecoglou's only fit centre-half at present.
Ben Davies and Emerson Royal have both been shoe-horned into central roles during Tottenham's dismal run of form, which has seen them only amass one point from their last five top-flight matches.
Meanwhile, Man United have been left short at centre-back due to injuries to Jonny Evans and Lisandro Martinez, while Raphael Varane has fallen out of favour and is expected to leave next year.
Both Spurs and Man United are also understood to be admirers of Nice's Jean-Clair Todibo, and the latter have apparently not given up hope of a January swoop for the Frenchman.