The Italy international joined the influx of Serie A players to arrive at the Tottenham Hotspur Stadium last summer, although he remained on loan with Udinese for another campaign.
After a positive farewell season with the Italian outfit, Udogie immediately became Spurs' first-choice left-back under Ange Postecoglou, which pushed Sergio Reguilon out of the door to Manchester United on loan.
Ryan Sessegnon and Ivan Perisic's injuries have also helped Udogie to cement a regular starting role, and the 21-year-old has one goal and two assists under his belt from his first 14 games for the club.
Udogie was a key component of the Tottenham team to take a whopping 26 points from their first 10 games of the new term, and he scored his maiden Lilywhites goal in Sunday's 4-1 thrashing of Newcastle United.
Udogie penned a five-year contract upon his arrival in North London, meaning that the left-back is not due to become a free agent until 2027, but according to Fabrizio Romano, a renewal has already been agreed.
The transfer guru states that Udogie will put pen to paper on a new "long-term" deal with Spurs, who will also be handing the left-back a pay rise as a reward for his stellar start to the campaign.
It is seemingly only a matter of time before Tottenham officially announce the left-back's new contract, which will see him become just the second player at the club to extend his terms this season.
Last week, Spurs confirmed that backup goalkeeper Fraser Forster had penned fresh terms until the summer of 2025, prior to which Alfie Whiteman's extension in February was their most recent renewal.
Ben Davies was the last outfield Tottenham player to sign on the dotted line in July 2022, but four members of the Tottenham first-team squad are currently due to become free agents next summer.
Exiled goalkeeper Hugo Lloris will be leaving for nothing in 2024 as things stand, although Newcastle United have been linked with a January move for the Frenchman following Nick Pope's shoulder injury.
Defensive duo Eric Dier and Perisic - the latter of whom is out for the season with an ACL injury - are also unlikely to be handed new deals, while fringe goalkeeper Brandon Austin is also about to enter the final six months of his deal.
Once Udogie's renewal is sealed, Tottenham are expected to turn their attention to the January transfer market, where a new centre-back and new winger could be targeted by Postecoglou and the sporting team.
Davies has been bumped down the pecking order by Udogie this term, but the Welshman has been forced to fill in at centre-back alongside Cristian Romero in recent weeks after Micky van de Ven was ruled out until 2024 with a hamstring injury.
Bournemouth duo Ilya Zabarnyi and Lloyd Kelly are both thought to be on Spurs' defensive shortlist, as are Nice's Jean-Clair Todibo and Atalanta BC's Giorgio Scalvini.