The troubled Prime Minister needs support from across the House to pass her EU Withdrawal Agreement Bill.
Mrs May said in The Sunday Times she is asking MPs to vote on an “improved packaged of measures that can win new support” and she is not asking MPs to “think again on same deal”.
The new bill is expected to include new measures on protecting worker rights, which is an issue where the two main parties nearly agreed.
Mrs May said: “I still believe there is a majority in parliament to be won for leaving with a deal.
“When the Withdrawal Agreement Bill comes before MPs, it will represent a new, bold offer to MPs across the House of Commons, with an improved package of measures that I believe can win new support.”
MPs are due to vote on the bill at the beginning of June and if the bill fails to pass, the UK will leave the EU on October 31 without a deal.
Mrs May’s offer to MPs comes after Labour and Tory talks ended without a deal.
Labour leader Jeremy Corbyn said talks had “gone as far as they can” and Mrs May said the lack of common ground had made talks “difficult”.
The latest Opinium poll for the Observer has the Tories behind Nigel Farage’s new Brexit Party ahead of this week’s EU election vote.
Bret Secretary Stephen Barclay has warned the Government they would need to increase planning for a no-deal exit from the EU if MPs vote against the Withdrawal Agreement Bill.