The 18-year-old, who was part of the Under-18 side last season, was initially told he would not be offered a contract at Glanford Park.
However, boss Alan Knill asked the midfielder to return for pre-season training, even handing him a squad number.
But Matthews has now been told he does not have a future with the League One club.
Knill told the club's official website: "We just felt it would have taken him too long to get into the first team.
"When we spoke to him last Friday we explained we don't think he is up to the level for when we need him."