The England international was a key cog in Antonio Conte's three-man defensive wall but has been consigned to a bit-part role since Ange Postecoglou took charge.
Dier - whose showings in the 2022-23 season were often criticised - had already fallen down the pecking order in the final weeks of last term under Ryan Mason, although it then emerged that he would require surgery on a groin injury.
The 29-year-old did not make Postecoglou's first four Premier League squads during his recovery, while he also missed out on some valuable minutes in an EFL Cup second-round loss to Fulham.
Since completing his rehabilitation, Dier has only been an unused substitute in five top-flight games and still awaits his first competitive minutes under Postecoglou, who has quickly settled on Cristian Romero and Micky van de Ven as his first-choice pairing.
Tottenham's defensive ranks are noticeably depleted, though, and Dier represents the most senior backup option to Van de Ven and Romero should one or both players sustain injuries between now and the end of the season.
Alongside Dier, Postecoglou's only other reserve options at centre-back are 18-year-old Ashley Phillips and left-back Ben Davies, who would sometimes be deployed in a three-man wall under Conte.
There has been talk of Tottenham potentially entertaining offers for Dier in January amid links with a return to Sporting Lisbon, but their defensive shortages makes such a scenario appear unlikely.
Now, a fresh report from Football Insider claims that Dier is also not keen on the idea of a mid-season exit and would rather depart the club for nothing when his contract runs out at the end of the season.
The ex-Everton youngster decided against moving on in the summer in order to prove his worth to Postecoglou, but an exit at some point in 2024 is now seen as inevitable amid his ongoing struggles.
Dier was said to have been in talks over a new deal at one stage, but such discussions have allegedly now collapsed, and the Englishman wants to leave as a free agent in order to maximise his future opportunities.
Dier - who started out as a midfielder before transitioning to a defensive role - boasts 13 goals and 12 assists in 360 games for the Lilywhites, but he has not won a single major trophy at the club.
Tottenham are already believed to be planning for life without the 29-year-old, identifying Borussia Monchengladbach's Ko Itakura and America's Sebastian Coates as possible defensive reinforcements.
A January deal for Galatasaray's Victor Nelsson was also mooted, but the North London giants apparently have no plans to pursue a move for the Denmark international in 2024.
Tottenham remain unbeaten in the top flight under Postecoglou can return to the summit of the Premier League table with victory over Mauricio Pochettino's Chelsea in Monday's London derby.