The former England international is a free agent after being released from Sunderland after five years on Wearside.
Brown has been training with Blackburn's U-23 side in order to try to gain a contract with the Championship strugglers and manager Owen Coyle confirmed that he would like to make the former United man a Blackburn player.
"As soon as I get the green light from the owners that I can get that over the line, I'll pursue it vigorously," Coyle told 'BBC Radio Lancashire'.
"The proposal has been sent, it's just to come back with a yes or a no. We kick on from there".
Despite, being 36, Coyle has no worries over Brown's fitness.
"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.