The 29-year-old has spent almost decade in North London and has made a total of 364 appearances for Spurs across all competitions, but he has fallen down the pecking order since the arrival of head coach Ange Postecoglou.
Dier has made just four Premier League appearances so far this season and Postecoglou has preferred to play full-backs Ben Davies and Emerson Royal in central defence over the England international in recent weeks.
Cristian Romero and Micky van de Ven established themselves as the first-choice centre-back paring earlier this season, but both players are currently sidelined with injuries.
Dier is out of contract in June 2024 and FootballTransfers claims that West Ham have been in touch with Tottenham to discuss his availability.
Hammers boss David Moyes, is said to be impressed with Dier's defensive abilities and versatility, and believes the 49-cap England international would be a suitable addition to his first-team squad.
Elsewhere in the Premier League, Newcastle United are reportedly interested in taking Chelsea midfielder Andrey Santos on loan.
The 19-year-old joined Chelsea from Brazilian club Vasco da Gama for around £12.5m in January last year, before completing a season-long loan move to Nottingham Forest last summer.
However, Santos has only made two first-team appearances for Forest, including one seven-minute substitute outing in the Premier League, and he has been tipped to return to Chelsea in January to assess his options.
According to journalist Ben Jacobs, via Football365, Newcastle hold a long-standing interest in Santos and have enquired about his availability.
Chelsea are said to be planning to terminate Santos's loan deal at Forest, but it remains to be seen whether a winter-window switch to St James' Park is realistic.
Eddie Howe is keen to bolster his squad in January amid an injury crisis, and midfield reinforcements are believed to be high on the agenda, with Manchester City's Kalvin Phillips another name said to be firmly on the club's radar.
Over at the City Ground, Nottingham Forest have reportedly opened talks with Paris Saint-Germain about re-signing experienced goalkeeper Keylor Navas.
The 37-year-old spent the second half of last season on loan with the Tricky Trees, making 17 appearances and helping the club avoid relegation from the Premier League.
Navas has since failed to make a single appearance for PSG this season, largely due to a spinal injury, but nevertheless Gianluigi Donnarumma is considered the club's number one goalkeeper.
The Costa Rican has since returned to training and has been tipped to leave PSG in search of regular game time, with Nottingham Forest keen to lure the goalkeeper back to the City Ground.
Football Insider claims that Forest have opened talks with the Ligue 1 champions over a January deal for Navas, with new head coach Nuno Espirito Santo on the lookout for a goalkeeper who is capable with the ball at his feet.
Current number one Matt Turner has made a number of costly errors so far this season, while Odysseas Vlachodimos, a summer signing from Benfica, has failed to make the desired impact at the City Ground.