Holden has been on trial with Wanderers after leaving the Houston Dynamo of Major League Soccer, although the 24-year-old American is currently nursing a slight thigh injury.
Both players are set to sign until the end of the season and will become Coyle's first new recruits since he was appointed manager at the Reebok Stadium earlier this month.
"I expect both deals to be done today," Coyle said.
"Stuart is obviously injured at the moment but with Vladimir there is just that final bit of paperwork, and then I would expect him to be in the squad (for tomorrow).
"He is a very positive player. He is a player who likes to get at full-backs, who likes to get crosses in and shots in.
"He is the type of player that I want at the football club - one that excites the fans. I also believe there is an edge to his game and a quality that will help the ones we already have.
"There is an incentive for Stuart to try and get himself in the team. He's had a little thigh knock for the last three or four days which has curtailed his training a little bit, but he did ever so well in the first week and he comes looking to push his career on.
"He has done very well in the MLS and he wants to continue that development.
"He is hungry, he has desire and he has ability, so ultimately when he's fit, it will be up to him to us what he has got."
Bolton 4/5, Draw 5/2, Burnley 7/2