Barton sent nine months at Turf Moor last season, helping them win promotion to the Premier League, but had his Rangers contract terminated earlier this month.
"It's a situation where, if he called me and said 'can I train?', we'd help him out the best we could," Dyce said.
"There's lots of players in my past I've helped out. If he felt he needed a base to get fit, among many other players I've helped out, I'd listen.
"Myself and my staff have helped out young players, old players, phone calls to other clubs. If Joey requires our support here, he'd get that."