Aboo Sa'eed reported that Gabriel came to the Prophet (ﷺ) and asked, "Muhammad, have you fallen ill?" He answered, "Yes." [Gabriel] said, "In the name of Allah, I exorcise you from everything that harms you; from every jealous soul and evil eye He will cure you; I invoke the name of Allah for you." [1]

Is this conversation present in the Qur’an?

Revelation from Angel Gabriel is not necessarily a part of the Qur’an. The Prophet (ﷺ) received three types of revelation (wahy): Qur'an, Hadith Al-Qudsi and Hadith An-Nabawi. Revelation is not restricted to the Qur'an alone.

Reference:

[1] Al-Musnad; c.f. Sahih Muslim, no. 5425