Lampard has emerged as one of England’s brightest young managers since cutting his managerial teeth at championship side Derby County two years ago.
After taking the Rams to the cusp of Premier League promotion, Lampard returned to Chelsea last season and guided his former side to a top four finish as well as an appearance in the FA Cup final despite operating in challenging circumstances.
The 42-year-old has further enhanced his reputation this term, with Chelsea sitting prettily in third place on the league table and into the knockout stages of the Champions League in convincing fashion.
Ivanovic, who has returned to the Premier League with a move to West Bromwich Albion, won the Premier League, FA Cup, UEFA Champions League and Europa League as a teammate of Lampard at Chelsea, and the Serbian has backed his former colleague to take charge of his country at some point in the future.
"When Frank decided to become a manager, everyone who knows him knew he was going to be a success," the 36-year-old was quoted by the Daily Mail.
"He is the right person in the right place, not just for Chelsea. I hope he will stay at Chelsea for life, but for sure he could give to his country and be manager of the England national team.
"He knows football and has great ideas. I watch his interviews and you can see he understands the game, the things he needs to do and how to give belief to the group.
"It's a massive job to understand football and to make the team play and work like you want. He has a good group of people around him to help him. He will be a success.
"He fully deserved to be Chelsea manager, not just because of his name. Of course I wish him all the best and for me he will always have a huge part [to play]."