Joe Anderson said the city council would launch a feasibility study before submitting a bid.
Hosting the event "would reflect the city's growing confidence and expertise in organising large events", he said.
Mr Anderson's announcement came three days before voting to select Labour's candidate for the Liverpool city region metro mayor election closes.
MPs Luciana Berger and Steve Rotheram are the other hopefuls.
The UK's nomination for a host city will be decided in 2018, with the successful host named by the Commonwealth Games General Assembly in 2019.
Mayor Anderson said: "Liverpool is an ambitious city and I believe we have an enormous amount to offer when it comes to hosting an event of this scale, which would be an incredibly important catalyst for regeneration, investment and raising the profile of sport."
Heptathlete Katarina Johnson-Thompson, boxer Tony Bellew, and former footballer Jamie Carragher are among the ambassadors for the proposed bid.
The last British city to host the games was Glasgow in 2014 although England last held it in Manchester in 2002.
Manchester City Council leader, Sir Richard Leese, said that despite "a long tradition of sporting rivalry... Liverpool's bid to host the 2026 Commonwealth Games has Manchester's wholehearted support".
In July, the Welsh government dropped plans to bid for the event, blaming the cost and uncertainty after the Brexit vote.
Birmingham City Council leader, councillor John Clancy, said in April that he was "open to persuasion" after the city was encouraged to bid but he believed it "would detract from our immediate priorities".
Last year, it was announced that South Africa would host the event in 2022 after the Canadian city Edmonton withdrew its bid due to cost. The awarding of the games to Durban followed concerns from the Commonwealth Games Federation about a lack of interest from member countries in hosting future competitions.
Liverpool has recently held a number of large spectator events including when 1.2 million spectators watched ocean liners gather to celebrate Cunard's 175th anniversary last year.
In 2014, a giant puppet show to mark the 100th anniversary of World War One attracted about a million visitors.
There's nothing new in Mayor Anderson's desire to bid for Liverpool to host the Commonwealth Games in 2026.
It was one of his pledges when he successfully ran for re-election as mayor of Liverpool in May.
It's also no coincidence that he is a candidate in an election - which ends on Friday - for Labour's candidate to be metro mayor of the Liverpool city region.
Evertonians will be desperate to hear that a new stadium for the club will be part of the plans, but anything concrete is a long way off.
The Mayor's declaration of intent brings local athletes on board - but will also provoke those who think at a time of austerity, the city can ill afford to be spending money on an international sporting event.
But then, people said that about Liverpool's bid to be European Capital of Culture - which went on to be a huge success.
Liverpool is planning a bid to host the 2026 Commonwealth Games, the city's mayor has said.