Mundy, 28, resisted temptations to move back home to Victoria in 2010, despite significant interest from Essendon and Hawthorn.
He was arguably the Dockers' best player in the Grand Final loss to Hawthorn and Barlow believes his midfield colleague will remain a Docker for life.
"The footy club are really keen to keep him around and I think David is more than happy to stay around," Barlow said.
"The beauty of free agency for the boys is they can use their power and David has been in the system for a long time and is a highly regarded player within the club, and within the state.
"[He] is starting to get some real recognition outside, so I don't think he'll go anywhere with the places we're hoping this club is heading towards.
"It's exciting times ahead and David is a big part of that."
Barlow signed a contract extension on Tuesday to remain at the club until the end of the 2016 season.
The 26-year-old midfielder, originally from Shepparton in Victoria, says he understands how players can be tempted to move home if they are drafted to interstate clubs.
But Barlow believes the culture at Fremantle and the potential success of the club is too hard to walk away from.
"I can definitely see how players across the competition have those temptations [to head back to home states]," Barlow said.
"You see a lot of it. We saw a lot of it from Brisbane this year as probably the example where some young players headed home.
"From my point of view and the club's point of view here, especially over the past four or five years, we have built a really strong culture and, I suppose, a group of men from the players to the coaching staff who really want to be involved with each other and play together and train together and achieve something special together.
"You mention guys like David, a few years ago there was probably the temptation of family and friends and whatnot.
"But you would like to think that you make a strong connection with the club you're at and in the west that is no different with the Fremantle Football Club.
"I have made a strong connection with the boys and the coaching staff and even people outside of the club. It's a great place to live and work."
