"An offer has been made and we are waiting to hear from Adam," said chief executive Gethin Jenkins in the South Wales Echo.
Matthews is now weighing up his options.
He's just 19 and will be allowed time to decide by the club. He's appeared in 11 games so far this season and seems a level headed young man.
He said: "I've played in quite a few matches this season and I'm making progress.
"I have a long way to go to reach my potential and I can't expect to play every week with quality defenders like Kevin McNaughton and Lee Naylor in front of me.
"Every young player wants to be involved all the time, but the team are winning games and stand second in the table.
"I won't be moaning about not starting, but I will also be ready if the gaffer needs me. There is a long way to go this season."