The 1995 World Player of the Year added weight to the Manchester City coach's chances of succeeding Claudio Ranieri at the Ligue 2 leaders
The Ligue 2 side, taken over by Russian billionaire Dmitry Rybolovlev in December 2011, are leading the French second-tier standings with nine matches remaining but are expected to oust current boss Claudio Ranieri in the summer.
Despite some fervent denials from the former Inter boss, Mancini has been tipped to succeed Ranieri at Monaco this summer, and Weah has backed him as a prime candidate for the role.
"Mancini would be a good appointment for Monaco, they have an interesting history, and of course, Arsene Wenger was one of their former coaches - and probably their most important - but since he left they have struggled," Weah told talkSPORT.
"I hope the new owners can bring them back to their former glories. They want the team to grow and my heart goes out to them because Monaco were my first club. We all want to see them back amongst the best teams in Ligue 1."
Weah enjoyed a successful three-year spell between 1992 and 1995 at Paris Saint-Germain before moving to England in the early 2000s with Chelsea and City - all of whom have since benefitted from overseas investment - but he admits he holds the Blues closest to his heart.
"The facilities are good, but it's a whole new Chelsea from the one I knew. It has been a beautiful and huge investment, and above all it's a good thing for the future of Chelsea," he added.
"I've watched [City] on TV and they are very different now [from when I was there] but their investment has been for the good of the game.
"I've not had a chance to speak to anyone at City recently but they were very good to me. Chelsea were different because I had a personal relationship with them and I've maintained my contact with them.
"Paris are doing very well and we must congratulate them, but we all know that they have very good resources. I hope they continue to do well. The Champions League is difficult to play in but they have the potential to win it."
The Liberian, who has since turned his hand to politics in his home nation, became the first African recipient of the Fifa World Player of the Year award in 1995, but he concedes that the continent is no longer considered a superpower in world football.
"First of all, congratulations to Nigeria [for winning the Africa Cup of Nations]. They started slowly but in the end they became champions. I'm disappointed though because it was a poor Afcon," Weah lamented.
"The teams were not as strong as I thought they'd be but I hope the next one will be more interesting. There were some good things like the smaller nations such as Burkina Faso showing that African teams are improving, but there's no big African teams anymore.
"I believe there is still a lot of African talent around, but there always has been. It's a continent full of talent and people, and generations have come and gone, but it'll never go away."