Spurs are firm fans of the teenage defender and want to make sure they snap him up this summer.
They have held talks with Udinese and, according to Sky Italia, a verbal agreement is now in place to take Udogie to north London.
The deal will see Tottenham loan Udogie back to Udinese to see out the season, before he then arrives in England next summer.
Now the two clubs will work on putting down on paper what they have verbally agreed as a deal is then put over the line.
Spurs will be hoping to see Udogie continue his development in Italian football, where he is expected to feature on a regular basis for Udinese.
Last term he clocked 35 appearances for Udinese in Serie A, scoring five goals in the process.
The 19-year-old has been capped by Italy up to Under-21 level and is tipped for a bright future.