Police arrested a 31-year-old man in connection with the incident in September. He has been bailed while inquiries continue.
A Tottenham spokesman said on Tuesday: "We have been providing support for Destiny and his family since the incident and will continue to do so.
"Given this is a legal matter, we cannot comment any further."
Police were called late in the evening on September 6 to reports that a man in his 20s had been threatened with a gun in a north London suburb popular with Tottenham and Arsenal players.
A spokesman said: "Officers spoke to the victim and during the course of their investigation it was also reported another man in his 20s had also allegedly been blackmailed and threatened by the same individual.
"No injuries were reported in either incident.
"A 31-year-old man was arrested on Monday, September 8 on suspicion of possession of firearms with intent, blackmail and driving without a licence."
Udogie started Tottenham's 4-0 Champions League home win over Copenhagen on Tuesday.
