Udogie impressed for Udinese last season and his performances have put him on the radar of several sides.
Tottenham are keen to continue making additions and the 19-year-old is wanted in north London, with Spurs trying to put a deal in place for his signature, according to Sky Italia.
Spurs are pushing hard to find an agreement with Udinese for Udogie, which could come in at the €25m mark, and would even be willing to let him remain at Udinese on loan next season.
It is claimed Tottenham are showing the strength and determination needed to win the race for Udogie, but they do face competition.
In recent days, Brighton, Manchester City and Inter have all made enquiries about the situation regarding Udogie.
The trio of sides rate the teenager highly and are determined to be kept informed of his availability.
Udogie made 35 appearances in Serie A for Udinese over the course of last season, scoring five times and providing three assists for his team-mates.
He scored and assisted on the final matchday of last term as Udinese crushed Salernitana 4-0.