Mosimane has stamped his authority since taking over the helm at Mamelodi Sundowns in 2012, winning two league titles and two domestic cups thus far.
Barker, who lead South Africa to their maiden Africa Cup of Natins triumph in 1996, believes 'Jingles' has improved as a coach but more importantly possesses all the qualities to again lead Bafana in the future.
"I have said many, many times: there is a big difference between being a club coach and an international coach. There’s a lot of pressure from all around the national team coach.
"You’ve got to be a tactician and somebody who can talk to the press, so it’s really tough job.
"It would be the right thing to do; [for Pitso] to come back and establish himself as an international coach again."
Mosimane previously served as national team assitant to World Cup-winning Brazilian coach Carlos Alberto Perreira, before taking over the head coach position after 2010 FIFA World Cup on home soil.
However, the former SuperSport United mentor was later sacked after the team failed to qualify for the 2012 AFCON finals in Equatorial Guinea and Gabon.