Last season's Championship play-off winners have already signed Tyrone Mears, Steven Fletcher and David Edgar as they prepare for life in the top flight.
Coyle remains keen to capture additional new faces and is hopeful he will be able to bring a couple of players to Turf Moor before kicking off the new season at Stoke on August 15.
"We are trying to get one or two in," he told Sky Sports News.
"But other factors need to come together for that. One, the club has to accept there has been a bid and, two, the player has to be willing to join.
"We will continue, in a sense, to try to complement the squad that we have."
Burnley have been reported to be considering a second bid for Brian Easton after failing in an initial attempt to secure the Hamilton Academical full-back.
But while Coyle is happy to admit he is eager to increase the size of his thin squad, he remains tight-lipped surrounding speculation.
"We are always going to be linked with players, that is understandable," he added.
"We will continue to try and do it in a professional manner from where the club is concerned and if we are able to reach an amicable agreement then we will announce it.
"You are always going to be linked, that is the nature of the build-up to the season. I don't want to enter into that, especially with players at other clubs, and will continue not to.
"I would still like add to the squad. I can't say whether it is three, four, five or whatever.
"I am still looking to improve the squad, help the lads that we already have and create real competition for places."