Mr Gove and the Chancellor have been at loggerheads over putting fishing waters on the negotiating table.
A source close to the Environment Secretary Michael Gove said giving EU members states access to the British waters would betray the result of the referendum.
The source said: “Michael has been clear that we need to take back control of our waters.
“The suggestion of the same access in future is totally unacceptable and goes against the result of the referendum.”
Mr Hammond’s suggestion comes after the seventh Cabinet “Road to Brexit” speeches where he demanded a future deal for the UK’s banking sector.
The Chancellor noted the EU’s pleas to continue fishing in UK waters.
He said: “Of course we would be open to discussing with our EU partners about the appropriate arrangements for reciprocal access for our fishermen to EU waters and for EU fishermen to our waters.
“We would have to negotiate the basis on which such an arrangement could be fair and appropriate for us.”
His comment came just days after staunch Brexiteer Jacob Rees-Mogg said: “The fishing community should not be used as an easy negotiating offer.”
Last night the Fishing for Leave group accused Philip Hammond of “testing the water to see if they can get away with selling out coastal communities.”
Chairman of the group Alan Hastings said: “For an EU that’s keen to avoid ‘cherry picking’ they are after the sweetest of them all – to continue pillaging £3-4 billion pounds of fish from our rich resources that were sacrificed to the EU to join.
“The EU has put a gun to Mrs Mays head with this demand which is now an immediate ‘acid test’ that she either resoundingly rebuffs or capitulates to – the time for platitudes is over.”
But Brussels said a trade deal with the UK will be conditional on EU fisherman maintaining ongoing access to waters.
One official told The Sun: “I find it very difficult to imagine there would be an agreement on that without also an agreement on mutual access to fishing waters, that’s a political reality.”
While addressing HSBC bankers, The Chancellor said the booming City of London was a “European asset” but one where the UK taxpayer bared the risks while the whole continent benefitted.
He added: “This is not a zero-sum game where any loss of market share in London is automatically a gain to another EU capital.”
In a reference to the Berlin Wall, the Chancellor warned a new “Iron Curtain of regulation” would hit the whole European economy.
He said: “Modern Europe is, quite literally, a testament to the benefits of tearing down walls.
“Let us not now propose new barriers where there need be none.”