Greater Manchester Police (GMP) said the man had been "eliminated" from its investigation.
The victim, found with a head injury on Thursday in a play area in Rochdale, has not yet been formally identified.
A Facebook post on Friday from Jalalia JaamÃ© Mosque said Koran reader Jalal Uddin "passed away last night".
It is understood Mr Uddin was a qari (Koran reader) at the mosque. He is believed to have been on his way home from a friend's house when he was assaulted between 20:40 and 20:55 GMT.
Det Ch Insp Terry Crompton of GMP said: "We are still working to establish the exact circumstances surrounding how Jalal came to suffer his injuries and we are keeping an open mind as to the motivation behind this attack, with a number of lines of inquiry currently being investigated.
"Understandably, news of this attack has caused concern in the local area and we have extra patrols in place to try and reassure the community.
"There has been a lot of speculation on social media about what happened and what may have been the reason for this attack, but I would urge people to refrain from making assumptions and please contact us with any information they have."
A 31-year-old man arrested on suspicion of murdering a prominent member of a Greater Manchester mosque has been released without charge.