USA international Ream has been lined up as a replacement for Gary Cahill, who has finally compleetd his move to Chelsea.
The New York Red Bulls defender had also attracted interest from Arsenal and West Brom, but he could sign for Bolton in the next few days.
"He is a player that we would love to bring to the football club and hopefully in the next few days that can come to fruition," said Coyle.
Meanwhile, speculation had claimed that Coyle had opened talks about a £4million deal to sign Mexico international Dos Santos from Spurs.
However, while describing the former Barcelona youngster as a "top player", Coyle cooled reports that he is already in discussions regarding a deal.
He added: "We haven't been speaking to the lad. There are fantastic young players out there in the Premier League and he is certainly one of them, but it is just speculation.
"There is no doubt that he is a top player, but there are many top players out there."