Is there a specific time to visit the Prophet's Mosque?

Visiting the Prophet's Mosque, peace and blessings be upon him, is recommended at any time of the year, and there is no specific time for it. What is rumored, that its visit should be after or before Hajj, has no evidence. Scholars mentioned visiting the Prophet's Mosque in the rites (of Hajj) because it was difficult for people to travel to it, so they would combine its visit with Hajj. However, the visit has no relation to the rites (of Hajj).