Bristol wants to host matches in the 2021 Rugby League World Cup at Ashton Gate, BBC Radio Bristol reports.
England was chosen to host the tournament in 2016, ahead of a rival bid from the United States and Canada.
Bristol City Council want to submit a bid to the Rugby Football League by July, with the RFL set to reveal their chosen cities later this year.
“We want to attract more world-class events to the city,” a Bristol City Council statement said.
“With the cycling grand prix happening later this year and the announcement of the Cricket World Cup coming to the city the year after, there is plenty to get excited about over the next two years.”
No professional rugby league teams play in Bristol, but that could change after 2019, with the Gloucestershire All Golds and Oxford planning to merge.
The two League One clubs’ proposal to form a new team has been accepted by the RFL, but they still need further financial backing.
The city of Bristol hosted a match during the 2013 Rugby League World Cup, with Bristol Rovers FC’s Memorial Stadium selling out for the USA’s 32-20 win over the Cook Islands.
This time, it is Ashton Gate – the joint home of Championship football club Bristol City and the city’s Premiership-bound rugby union side – which is being put forward.
Phil Cole, chairman of the Bristol Sonics, the city’s only current senior rugby league team, said: “It’s fantastic news. We’re delighted to see Bristol bidding again.
“We’re hopefully going to be involved with the legacy side of things. There’ll be a campaign over the next few years to increase participation and get more women involved in rugby league too.
“It was a great success in 2013, when it was a wonderful evening at the Memorial Stadium. We’ve got a great bid, but it’s just a case of whether they’ll go for more games in the north.”
BBC Radio Bristol understands that the City Council and Ashton Gate Limited – who are working on the bid collaboratively – are hoping to secure a package that includes a quarter-final.
The RFL received £25m from central government to support its bid to stage the tournament, and plans to host 80% of games in Lancashire and Yorkshire.