The 27-year-old continued to form his effective midfield partnership with Declan Rice in the 2021-22 campaign and tallied six goals and one assist from 51 games in all tournaments.
Soucek started nine games for the Hammers en route to the semi-finals of the Europa League, and he featured from the first whistle on 34 occasions in the Premier League.
Soucek penned a four-year contract at the London Stadium following his arrival from Slavia Prague on a permanent deal, and those terms are due to expire in the summer of 2024.
West Ham are understood to have opened discussions to extend Soucek's contract in the English capital, although such talks supposedly stalled last week.
Soucek and manager David Moyes have allegedly seen their relationship deteriorate, leading to widespread uncertainty over the Czech Republic international's future.
According to Football Insider, Tottenham have now been offered the chance to seal Soucek's signing by intermediaries, with the midfielder edging closer to an exit from West Ham.
The report adds that there is a "very real chance" that Soucek could head for the exit door, but tensions at board level between West Ham and Tottenham could make a move difficult.
West Ham's move to the Olympic Stadium did not go down well with chairman Daniel Levy, who is reported to have since blocked players from joining Spurs' capital rivals.
Soucek has now turned out for West Ham in 105 matches in all tournaments since his initial loan arrival in January 2020, scoring 19 goals and setting up two more.
Tottenham strengthened their engine room with the signing of Rodrigo Bentancur from Juventus in January, and the Uruguayan has since been an ever-present alongside Pierre-Emile Hojbjerg in Antonio Conte's side.
Bentancur's arrival has seen Harry Winks drop further down the pecking order, and the Englishman could be sold this summer, providing that Spurs' £25m valuation is met.
Winks's departure could tempt Conte into bolstering his midfield further, but a new centre-back is still thought to be the Lilywhites' priority after the capture of Ivan Perisic from Inter Milan.
Perisic's Nerazzurri teammate Alessandro Bastoni is thought to be Spurs' leading defensive target for the summer window, although the Italian is keen to remain at San Siro.
Tottenham are also expected to announce the signing of Fraser Forster from Southampton in the coming days, with the shot-stopper signing a two-year contract after leaving St Mary's.