With Major League Soccer currently in its off-season, Ream spent last week with West Brom keeping up his fitness, and this week is training with Wanderers.
Red Bulls sporting director Eric Soler has stressed the 24-year-old has made the trip to England to gain experience and that as far as he is concerned, Ream will be with the American club next year.
As a great admirer of the centre-back, that stance comes as no surprise to Coyle.
The Scot is keen to sign Ream, though, and has hinted it is something he may still look to pursue when the transfer window opens in a few weeks.
"Would we like to have him at the football club? Absolutely," Coyle said.
"Red Bulls have said that he is not for sale and that is totally understandable - I would say that about my top players.
"Tim Ream is an outstanding player. He is someone I have known about for a couple of years now and I have watched his games extensively.
"I can totally understand why the Red Bulls would say he is their player, because he is a prized asset.
"But he has come in here, conducted himself very well and shown his quality - he has a lot of similar qualities to (Bolton's USA international) Stuart Holden, in terms of mentality and how he sees the game and wants to progress, and those are attributes I love.
"He is a New York Red Bulls player and I wouldn't say anything else beside that because you have to respect that he has come in for a week's training with the permission of the club.
"We'll leave it at that for the moment, and we'll see what January brings."