After losing his place in the Lilywhites' starting lineup towards the end of last season, the Englishman was not even in the squad for Saturday's draw with Brentford in their Premier League opener.
Head coach Ange Postecoglou has insisted that Dier remains a part of his plans, but he is seemingly behind all of Cristian Romero, Micky van de Ven, Davinson Sanchez and Ben Davies in the pecking order.
According to 90min - via the Daily Record - Celtic, who previously took another centre-back in Cameron Carter-Vickers off of Tottenham's hands last year, are now lining up an approach for Dier.
However, Al-Nassr, Monaco and Crystal Palace are also thought to be keen on the 29-year-old, as are Sporting Lisbon, whom Dier represented for 11 years between 2003 and 2014.
Dier only has one year left to run on his contract at the Tottenham Hotspur Stadium, and he will likely be allowed to leave for free in 2024 if he is not sold in the coming weeks.
Sticking with the theme of Premier League outgoings, Aston Villa's Emiliano Martinez is believed to be on the radar of German champions Bayern Munich.
The World Cup-winning goalkeeper has been a key figure in the Villa Park backline since leaving Arsenal in 2020, keeping 39 clean sheets in 113 matches in all tournaments.
Martinez's Villa breakthrough has seen him cement his place as Argentina's number one, although he shipped five to Newcastle United in last weekend's crushing Premier League defeat.
The 30-year-old's efforts helped Villa achieve Europa Conference League football last season, but he has been persistently linked with an exit to a Champions League-competing club amid previous interest from Manchester United and Tottenham Hotspur.
According to TyC Sports, Bayern could now turn their attention to Martinez after losing out to Real Madrid in the race for Chelsea shot-stopper Kepa Arrizabalaga.
Bayern number one Manuel Neuer is still recovering from a broken leg, while Yann Sommer has left for Inter Milan, but the Bundesliga champions could be forced to make Martinez the most expensive goalkeeper of all time to bring him to Bavaria.
Elsewhere in Germany, Borussia Dortmund are not expected to sign Southampton centre-back Armel Bella-Kotchap this summer.
The 21-year-old is being tipped to leave the Saints following their relegation from the Premier League and had supposedly caught the eye of Edin Terzic.
According to Sky Deutschland, contact was made with Bella-Kotchap's camp, but Dortmund are refusing to meet Southampton's €20m (£17.1m) asking price.
The Saints are under no pressure to let the German leave, as his contract runs until 2026, and a move to the Westfalenstadion is now rated as "highly unlikely".
Bella-Kotchap joined Southampton from Bochum for €11m (£9.4m) last year and set up two goals in 26 games for the Saints during his debut season, starting 24 Premier League games.
However, the Germany international is yet to play for Southampton this term due to a hamstring injury, and he would be behind Mats Hummels and Nico Schlotterbeck in the defensive pecking order at Dortmund.
Finally, Monaco have reportedly reached a full agreement with Torino over a deal for Ivorian right-back Wilfried Singo.
The 22-year-old has risen through the Toro youth academy to make 109 appearances for the senior team in all competitions, scoring seven goals and setting up 10 more.
Singo has excelled as a wing-back in Torino's system and kept up his strong form in the 2022-23 season, registering two goals and three assists in 35 appearances.
However, the defender is now in the final 12 months of his contract, and according to transfer guru Fabrizio Romano, Monaco have struck a deal to sign him for €10m (£8.6m).
Singo will soon undergo his medical after putting pen to paper on personal terms, and he is snubbing interest from Atalanta BC to join the Ligue 1 club.
Monaco currently have Vanderson and Ruben Aguilar battling for the right-back spot, but Axel Disasi - who would sometimes fill in as a full-back - has departed for Chelsea.