Liam McGerrigan, 27, from the city, was pronounced dead at the scene after officers were called to Holyhead Road at about 22:10 BST on Thursday.
He had been stabbed in the chest. West Midlands Police said it was still keen to hear from anyone who may have seen an altercation near a church.
A 33-year-old man was arrested in the Tile Hill area on Friday.
Det Insp Shaun Egan, of West Midlands Police Force CID, said: "We believe there was an altercation and Liam staggered to an address in Holyhead Road where he collapsed.
"This was on a busy road and we believe there may be witnesses out there who can help with our investigation."
Police were called to Holyhead Road near the junction of Northumberland Road on Thursday night.
A man has been arrested on suspicion of murder after a man was found stabbed at an address in Coventry.