Last season's top scorer Dave Hibbert is considering new terms but is also in talks with Peterborough United.
New contracts have been offered to Kevin McIntyre, Shane Cansdell Sherriff, Benjamin Van den Broek and Harry Hooman.
Irishman Coughlan - who has played for Swindon, Livingston, Plymouth, Sheffield Wednesday, Burnley and Rotherham - was a keystone in Town's centre of defence.
The 35-year-old made 38 League and Cup appearances this season before picking up a late injury.
Midfielder Simpson, 19, is a product of the Blackburn Rovers academy and looked sharp in the first team after initially being given the chance by his father to train with the club.
In the hiatus between the sacking of Paul Simpson and the appointment of a new manager, the board is leading negotiations after taking advice from the club's remaining coaching staff, Dave Hughes and Mike Jackson.
"We as a board talk about the players we believe are vital for the club to go forward," said Shrewsbury vice-chairman Keith Sayfritz.
Source: BBC Sport
Source: BBC Sport