The pilot is being trialled at 12 surgeries near Forest Green’s New Lawn stadium in Nailsworth.
Tickets will be supplied by the club for free and the pilot will run all season – starting with the first home game against Yeovil on 16 August.
Mr Vince, who has owned the club since 2010, said: “I think it’d be a great thing if football clubs up and down the country could reach out to people and do this.
“Men typically don’t really talk about their issues, that’s the thing, and you get loneliness and things like that as well.
“I’ve had periods of my life where I’ve been a bit fed up, and excluded… a bit down from time to time, it’s easy to spiral downwards when you’re not in contact with people and I just wanted to do something with that.”
Forest Green reached League One for the first time in their history in 2022 before suffering two back-to-back relegations to end their seven-year spell in the English Football League.
Former Wales midfielder Robbie Savage was appointed as their new manager on 1 July.