Spurs are keen to snap up emerging talents and are set on beating off competition for the young left-sided player, who is on the books at Italian side Udinese.
Udogie was not involved for Udinese in their 2-1 win over FeralpiSalo on Friday, but he could well play in their Serie A kick-off next weekend against AC Milan.
That is despite Tottenham closing in and being close to a deal, with Udogie tipped to sign for Spurs early next week, according to Sky Italia.
Tottenham will pay a fixed fee of €20m for the defender, with a further €6m in bonus payments to take the total cost to €26m.
The terms of the deal will also see Tottenham then instantly loan Udogie back to Udinese for the season.
Spurs pulled off a similar swoop last summer when landing midfielder Pape Matar Sarr from French side Metz and then loaning him back.
Sarr is now at Spurs this summer, although he is wanted on loan by AC Milan; it remains to be seen if he lines up against Udogie.