Bolton are reportedly looking to sign the American international as a replacement for Chelsea-bound Gary Cahill.
Ream's agent Patrick McCabe has now admitted that talks with Owen Coyle's club are ongoing, with hopes of a deal over the next few days.
"Negotiations between Major League Soccer and Bolton are at an advanced stage and ongoing," Patrick McCabe told Goal.com.
"We hope to have a positive resolution for Tim in the next few days."
However, a source close to the player has told ESPNthat a deal could happen as soon as this weekend.
"There's not such a big gap between the sides," said the source.
"There's been significant progress in the last couple of days. Right now both sides are optimistic. There may be a little movement today. It could potentially be done today but more likely over the weekend."
Ream has been capped seven times by the US national side.