The Labour MP for Barnsley Central confirmed his plans at a meeting of local party activists after taking 'soundings from allies', according to Politics Home.
The website claims he is 'not expected to immediately quit Westminster' if he becomes mayor of the Sheffield City Region - which also takes in the South Yorkshire council areas of Barnsley, Rotherham and Doncaster - in May's elections.
Instead, it's claimed he plans to 'use the platform to campaign' for ministers to give the go-ahead for the mayor to be put in charge of devolution across the whole of Yorkshire.
At that point, it is understood he would announce his intention to quit the Commons in order to run for mayor.
Mr Jarvis is a staunch supporter of a 'One Yorkshire' vision combining the whole of the county.
Sheffield and Rotherham are in favour of the Government-signed South Yorkshire deal. Barnsley and Doncaster initially signed up the deal in 2015 but have since U-turned in favour of a county-wide proposal.
A poll of voters in Barnsley and Doncaster last month revealed they support having an elected mayor for the whole of Yorkshire, rather than just the Sheffield City Region.
The referendum turn-outs were less than 23 per cent but over 85 per cent backed a 'One Yorkshire' vision.
The Department for Communities and Local Government have previously said they would 'welcome discussions' on a widely supported greater Yorkshire devolution deal provided the Sheffield city region deal was 'not threatened'.
Former Sheffield MP and cabinet minister Richard Caborn and Sheffield councillor Ben Curran have already announced their intention to run.
The former Army major, who served in Iraq and Afghanistan, was tipped by many as a future leader when he was first elected in 2011.
He served on Ed Miliband's front bench as a shadow minister, but has fallen out of favour under Jeremy Corbyn's leadership.
Mr Jarvis did not confirm or deny the rumours when he was asked today.