The defender is currently without a club, after leaving Sunderland in the summer.
The 36-year-old has been without a club since departing Sunderland in the summer and has been training at Ewood Park since pre-season.
Coyle has told BBC Lancashire the deal will completed subject to approval from the club's owners the Venky's Group.
"As soon as I get the green light from the owners that I can get that over the line, I'll pursue it vigorously," he said.
"Wes is fit and ready to play. We've had daily chats, he is an outstanding man and think he is in good shape to play now," he said.
Brown injured his calf during pre-season training with Rovers but has proved his fitness with the club's under-23 side.
It has been a frustrating year for Brown, who has 23 England caps, as he has battled injuries.
The centre-back only made six appearances for Sunderland last season, and is looking to prolong his career in the Championship.
He started his career at Manchester United, winning five Premier League titles before slipping down the pecking order after Nemanja Vidic's arrival.
Brown then joined Sunderland from Manchester United in 2011 and went on to make 87 appearances before leaving at the end of last season.
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