Reid wants Shaw to work with The Sky Blues reserves side.
"I've had a quiet chat with Richard because I'd like him to be involved in some way," Reid told the club's official website.
"Bearing in mind his age it would be fair to say it would only be a one-year playing deal but having spoken to him he thinks he can certainly carry on playing.
"But he also works well with the kids and it would be great for us and them if he could take over the reserves.
"He's gone off to think about it for a while as you'd expect anybody to do and we'll meet up again in a couple of weeks or so."