Trotters manager Coyle has made an enquiry about taking Sturridge for the rest of the season after Chelsea, who are hoping to sign Fernando Torres from Liverpool, agreed the 21-year-old could go out on loan.
Coyle is a big fan of former Manchester City striker Sturridge and believes he would be a success at the Reebok Stadium.
"What I would say is Daniel Sturridge, as we all know, is a fantastically talented player," Coyle told Sky Sports. "A player who I believe is one of the best, if not the best, young strikers in the country and a player who I believe with the platform of the Premier League will get better.
"You are always looking to bring in players into the football club that can help. We certainly would love to add another player to the squad we have and we are doing our utmost to bring that to fruition.
"It won't be through lack of effort or want of trying but there are still a few boxes to be ticked before that can happen."