The 32-year-old joined the Cobblers in September on a short-term playing contract before becoming a coach.
"He wanted to play so we had an agreement that if a club came in for him we would let him go," Cobblers boss Ian Sampson told BBC Radio Northampton.
"Hopefully we will have a new coach in place in the next few days."
Brown has made almost 300 senior appearances for Colchester, Hibernian and Brentford but struggled to break into the Northampton team due to the form of Chris Dunn.
"Dunn has worked his socks off and regardless of who has been coaching him he deserves most of the credit," said Sampson.
"Simon helped Chris but Simon also wants to play.
"We amended his playing registration in January and now this opportunity has come his way we wish him the best of luck."
Source: BBC Sport
Source: BBC Sport