Holden was set for talks with Burnley before Coyle took over the reigns at the Reebok last week, with Blackburn also rumoured to be monitoring the situation.
Bolton now appear in pole position to sign the 24-year-old as Coyle seeks his first signing as manager of the club.
"Stuart's had three sessions with us and he will be with us for the rest of the week so we can assess him," Coyle confirmed to Manchester Evening News.
"He was one of the top performers in the MLS last season and has a lot of talent."
Holden, who was born in Aberdeen, has 12 international caps with two goals to his name and could face England when the nations meet at this summer's World Cup.
Meanwhile, Coyle has assured Kevin Davies he will remain club captain despite a new management set-up at the Reebok.
"It was never up for debate as far as I was concerned," added Coyle. "Kevin will be my captain.
"He has been a top performer in the Premier League for so many years, a fantastic player. And he's a fantastic leader and the type of person I am looking for at this club."
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