Mr Bainimarama made the announcement at a gala dinner marking the one-year anniversary of Fiji's historic win at last year's Olympic Games in Rio.
He said Fiji has been known as one of the finest exponents of running sevens rugby for decades and had become a dominant force on the international stage.
However, he bemoaned the fact the country didn't currently have a major international Sevens event placing them properly on the world stage.
"We do not have a major Sevens event that befits our position as Olympic Men's Rugby 7s Champions," Mr Bainimarama said.
Once the next bidding process commences, the Fiji Rugby Union and the government will submit a bid.
The Prime Minister, who is also the President of the FRU, said the country would look to put its best foot forward to host such an event.
"The opportunity to host a leg may be as early as 2020, it may be later, but we want Fiji to be ready when that time comes," Mr Bainimarama said.
The chairman of the FRU, Commander Francis Kean, said his board was making great strides on many fronts in becoming more professional citing a recently approved strategic plan which identified hosting of a leg of the Sevens Series as a key priority.
"The benefits of hosting a leg are truly significant," Mr Kean said.
"From the financial benefits to our economy flowing from the tourism and spending, to the massive global exposure of such an event, hosting a leg of the World Sevens Series positions our country favourably alongside the current other 10 cities.
"Plus, it gives our Sevens team a chance to play in front of a home crowd, in front of their families and friends."
Mr Kean said the FRU will be investing a lot of time, energy and resources over the next six months towards submitting a compelling bid.
Currently the HSBC World Sevens Series is played in 10 cities; Dubai, Cape Town, Sydney, Hamilton, Singapore, Hong Kong, Las Vegas, Vancouver, Paris and London.
The cities selected by World Rugby to host a major event would need to satisfy a wide range of criteria including venue, accommodation and potential attendance.
Mr Kean said the FRU was announcing its intention to bid when the opportunity arises once current hosting agreements expire in 2019.
Photo: PHOTOSPORT Fiji on the medal podium during the 2016 Olympic Games