The proposal sparked a massive backlash from pro-Brexit ministers in the British government cabinet, Bloomberg reported.
Brexit uncertainty has grown in recent weeks after the breakdown of talks between May and the opposition Labour party.
That has set the stage for the thrice-rejected fail to fail again if, as planned, it is put to vote in parliament next month.
Those concerns have weighed on the pound as the rejection of the deal yet again would likely pave the way for May to be replaced by a more hardline eurosceptic, possibly Boris Johnson.
"May's latest proposals seems to be aimed at wooing over some of the opposition to support her deal but the opposition from her cabinet is dampening some of the gains," said Lee Hardman, an FX strategist at MUFG based in London.
The pound rocketed 0.7pc to $1.2815 from $1.2725, its highest since Friday. It later gave up most of those gains to trade at $1.2769, up 0.4pc on the day.
Versus the euro, sterling jumped half a percent to 87.255 pence before settling at 87.52 pence, up 0.3pc from its earlier level.
The jump in the pound rippled over to the wider foreign exchange markets, sending the British currency surging against the Japanese yen and the Swiss franc and pulling the broader dollar index back into negative territory.
Positioning indicators were broadly neutral, with long positions in the pound being pared back in recent weeks, leaving the pound vulnerable to large swings either way.