His comments were echoed by former Brexit secretary David Davis, who quit the Government over the Chequers plan which would see Britain maintain a "common rule book" with the European Union for trade in goods and agriculture.
Mr Baker, a former chairman of the influential pro-Brexit European Research Group of Conservatives, urged Mrs May to negotiate a free trade agreement instead of the Chequers plan.
He said: "It is worth thinking about (the various scenarios) because everyone in Parliament who is enjoying making categoric statements about being against Chequers or against "no deal" is now loading the revolver for a game of Russian roulette, with a lot more than Brexit at stake".
"I hope that the Prime Minister will take on board what she's heard and chuck Chequers".
"We need, we must reach an agreement before the beginning of November".
London and Brussels say they want to get a divorce deal at the October 18 EU Council or at the latest by the end of the year.
"My view is we'll end up in a different place, a reset after Salzburg", he said. If leaders agree at the September 20 meeting, diplomats expect a final set of guidelines to be formally adopted at the October summit of European Union leaders, setting the stage for a special Brexit summit in November, where the two sides would aim to conclude talks.
The pound was up a cent against the dollar at more than $1.30 on the reported comments, with sterling was also up half a cent against the euro at just over €1.12.
Evacuations in United States ahead of Hurricane Florence
At least nine nuclear facilities also lie in the storm's path, including Duke Energy's Brunswick nuclear plant in North Carolina. About 10 million people live in areas that were under either hurricane or tropical storm warnings and watches Thursday.
Tottenham's Toby Alderweireld denies Manchester United summer move was close
To be in the first team again is a victory for me. "Regarding my future, everything that was said in the press was not right all the time ".
Tottenham battling with Barcelona and Real Madrid for Ajax wonderkid
The 21-year old midfielder, who plies his trade for Eredivisie giants Ajax has emerged as a top transfer target for Barcelona. Shortly after, he joined Ajax for whom he has made 37 first-team appearances, as well as 46 for Jong Ajax .
Michel Barnier, the EU's chief negotiator, said on Monday that a Brexit deal was possible "within six or eight weeks" if negotiators were realistic in their demands.
Even a small rebellion inside her party on a final deal could spell the end of her minority government and throw Britain's exit into chaos.
The rift in May's party deepened this week, with her former Foreign Secretary Boris Johnson, who quit the cabinet over the Chequers proposal, comparing May's plan in a newspaper column to putting a "suicide vest" on Britain's constitution.
Michael Gove, May's environment minister and a leading Brexiteer, told BBC radio: "I want to ensure that we get a solid vote, which I'm sure we will, when the prime minister brings back the treaty", adding lawmakers should rally behind May.
Andrea Jenkyns, who has submitted a letter of no confidence in May, told AFP the prime minister was "too dogmatic" to change course. Under Conservative rules, a leadership election is triggered if 15 percent of Conservative lawmakers, now 48 out of its 315 members of parliament (MPs), demand a vote of no confidence. "It'll be in November, when parliament votes on the deal", she said. The ERG on Wednesday unveiled its proposal for how Britain could leave the European Union without constructing a hard border between Northern Ireland and Ireland, one of the main sticking points in negotiations.
In a sign the Government remained committed to its plan, he told BBC's Andrew Marr Show: "I think the only deal that we've got on the table, that's the Chequers deal".
The proposal included using customs declarations ahead of travel and inspections of goods before they are shipped.