There are different sources for this narration, but those who are quoted in hadith collections don't quote Hudaifah () as the person who was asked by 'Omar (), it was narrated on the authority of Umm Salamah () in Musnad al-Imam Ahmad
عن أم سلمة قالت دخل عليها عبد الرحمن بن عوف قال فقال يا أمه قد خفت أن يهلكني كثرة مالي أنا أكثر قريش مالا قالت يا بني فأنفق فإني سمعت رسول الله صلى الله عليه وسلم يقول إن من أصحابي من لا يراني بعد أن أفارقه فخرج فلقي عمر فأخبره فجاء عمر فدخل عليها فقال لها بالله منهم أنا فقالت لا ولن أُبلِيَ أحداً بعدك
Where the word "munafiq" doesn't actually appear clearly, the hadith can be translated as follows (note this is my own translation and I've added some interpretation and explanation between brackets):
Umm Salamah said that one day Abdurrahman ibn 'Auf visited her and asked: Oh mother I'm afraid that I will be perished for my fortune, I'm the richest man among Quraish.
Umm Salamah said: Spend (from it) my son, for I heard the Messenger of Allah (peace and Allah's blessings be upon him) saying: "there will be among my Sahaba those who won't see me after I will leave them" (this is refering to munafiqyn).
When he left he met 'Omar and informed him (about what happened earlier). 'Omar then came and entered (asked for entrance in the house of Umm Salamah) and asked her: "By Allah am I among those?".
She replied: "No and I won't inform anybody after you!"
Imam at-Tabari narrated the same story in his al-M'ujam al-Kabir.
Al-Bazzar and Abu Ya'ala have compiled a similar narration according to al-Haithami in his majma' az-Zawaid, where he quoted it twice once the version of al-Bazaar and once with a slight difference in the narrator chain.
So the strongest evidences seem to point at Umm Salamah() instead of Hudaifah() to be the person asked by 'Omar ibn al-Khattab().
Note there's a hadith which was qualified as hassan by at-Tirmidhi saying:
Narrated Hudhaifah:
that they said: "O Messenger of Allah, if you were to appoint someone as a successor." He said: "If I were to appoint a successor over you, and you were to disobey him, you would be punished. But whatever Hudhaifah narrates to you, then believe him, and whatever 'Abdullah teaches you to recite, then recite it."
who compiled an other hadith (only available in Arabic so far) saying instead:
... But whatever ibn Masu'd narrates to you, then believe him ...
The first narration might be a kind of source for the companions and tabi'in to have trust in Hudhaifa's narrations, but note that this hadith is narrated by Hudhaifah himself and there is no consensus about the qualification given by at-Tirmidhi. Abdullah in this hadith from Jami' at-Tirmidhi refers to Abdullah ibn Mas'ud ().
What might be the source of your statement then?
What I could find so far is a statement in a biography of Hudaifah ibn al-Yaman in Imam as-Sakhawi's Al-Tuhfah al-latifah fi Tarikh al-Madinah al-Sharifah (التحفة اللطيفة في تاريخ المدينة الشريفة) where is quoted:
أن رسول الله صلى الله عليه وسلم - في عودتهم من تبوك - كان أسر إليه أسماء المنافقين، ...، وناشده عمر رضي الله عنه بالله: أنا منهم ؟ فقال: اللهم لا، ولا أزكي أحداً بعدك
(My own translation -take it carefully)
... The Messenger of Allah (peace and Allah's blessings be upon him) at his return from Tabook disclosed him the names of the munafiqyn, ... and 'Omar (May Allah be pleased with him) conjured him saying: "By Allah am I among them?"
He answered: "By Allah no, and I won't reveal it to anyone after you"
About two centuries earlier imam a-Dhahabi الذهبي in his siyar 'alam an-Nubal'a (p362-364 according to islamqa #144939 only in Arabic)سير أعلام النبلاء in the biography of Hudaifah quoted the same statement without quoting any narrator chain.
وقد ناشده عمر : أأنا من المنافقين ؟ فقال : لا ، ولا أزكي أحدا بعدك.
Here's my translation:
And 'Omar conjured him saying: "Am I among the Munafiqyn?"
He answered: "By Allah no, and I won't reveal it to anyone after you"
In the wikipedia Article on Hudaifah ibn al-Yaman you may read:
After Muhammad's death, the Khalifah often sought his advice concerning their activities but he remained tight-lipped. Umar, during his Khilafat was only able to find out indirectly who the hypocrites were by monitoring Hudhayfah’s attendance at the funeral prayer following the death of a Muslim. If Hudhayfah did not attend Umar refrained from performing the funeral prayer for that person.
Once Umar asked Hudhayfah if any of his governors was a munafiq. Hudhayfah told him that one was but declined to inform whom. Hudhayfah later said that shortly after their conversation Umar dismissed the person as if he had been guided to him.