The 23-year-old is currently Ligue 1's top scorer, having netted five times since the start of the season including the winning goal in the 2-1 victory over Marseille on Sunday.
Coyle admitted that he had lodged a bid for the Frenchman but was knocked back by the league leaders.
"We did make offers for strikers, because I do think we're short in that area, but it didn't happen," Coyle told Wigantoday.net. "There was one in particular, Emmanuel Riviere, who we bid £5m for a couple of weeks ago. But it's sod's law that he started the season with five goals in three games which put paid to that.
"He got a hattrick the other week,but even as late as Sunday there was a chance of it happening because they were chasing a lad at Atletico Madrid. We made our offer again, and he was only named on the bench against Marseille.
"I'm watching the game thinking: 'Fine, just don't put him on, we've still got a chance here.' But [Radamel] Falcao turned his ankle at 1-1, Riviere came on, left his two markers for dead and scored the winning goal against the top of the league! Claudio Ranieri rightly wants to keep him now, which I totally understand. If we could have brought him here it would have been an unbelievable signing for us."
Riviere joined Monaco in January.