Following their 2-0 victory at the Reebok Stadium on Sunday, a win for Wenger's team could take them above Chelsea to the top of the table.
It would mark quite a feat for the Gunners, who trailed Chelsea by 11 points in November after being beaten 3-0 by the Blues at the Emirates Stadium.
Since then Arsenal have gone eight games unbeaten in the league and, with the momentum building, Coyle believes they could well be champions come May.
Asked if he thought Arsenal were genuine title contenders, Coyle said: "They are, absolutely, and I think it's all credit to them.
"They are title challengers after not even just being written off - they were totally dismissed. I think they went 11 points behind at one stage and all credit to Arsenal and Arsene. He has galvanised them.
"They have had horrendous injuries to strikers, they have changed their forward line.
"People think they have an unconventional forward line with smaller types but their movement and their ability speaks for itself.
"So yes, they will be there until the end of the season, I've no doubt about it, and have a real chance of winning it."
On paper, the double-header against Arsenal looks like one of the worst assignments Coyle could have been handed as he gets his reign at Bolton under way.
Wanderers are second from bottom in the table and in desperate need of a win but the new manager believes there were enough encouraging signs from Sunday's game to suggest they are capable of pulling off a result at the Emirates.
"I don't think it is ideal for anybody but you have to play the best teams when you're asked to play," Coyle continued.
"We've been asked to play and we'll go there and play it and we'll do our best.
"It's a game that probably not a lot of people will give us a chance in but I believe we have.
"I think we offered enough the other day to show we can pose them problems and that is what we have to do - recognising that they have quality and we have to try and curtail that in some way.
"We will go there with a positive head on, look to commit players forward every way we can and try and achieve a positive result."