They expect the 62-year-old outgoing premier to take some time to consider her next role after her announcing her decision to stand down by the end of July yesterday.
And an official from her local party confirmed she intended to remain a backbench MP until at least the next general election.
But many Tories believe that the politician who has long trumpeted her commitment to duty and public service will not want to walk away from public life into political obscurity.
A minister said: “I could see Theresa accepting a peerage. She is a very traditional type of Conservative. The House of Lords would suit her.”
And a Tory backbencher said: “It would not surprise me at all if she went to the Lords.
“She is hardly likely to go on a world lecture tour like Tony Blair and David Cameron did.”
By convention, incoming prime ministers have tended to grant their immediate predecessors a peerage but John Major, Tony Blair, Gordon Brown and Mr Cameron all indicated in advance that they did not want the honour.
The only signal of Mrs May’s future plans yesterday came from Richard Kellaway, the chairman of Maidenhead Conservative Association in her constituency.
She rang him yesterday morning ahead of her resignation statement to confirm she would not be quitting as local MP.
“The main concern for us as her association is that she’s not going to resign her seat. She will carry on as a Member of Parliament, which is welcomed by us,” Mr Kellaway said.
“As the Prime Minister, she could go to the House of Lords if she wants to go that route and carry on, or she could stay a member of Parliament,” he said.
“Quite clearly, it’s a very troubling and difficult time for her and she’ll need to settle down and see what she wants to do.”
He described Mrs May as “circumspect” while campaigning yesterday in her constituency, but said she spoke “extremely well” in her statement outside Downing Street.
“It’s like any speech at a funeral or a wedding, even. You get through it,” he added.
Mrs May will remain prime minister until a successor is chosen by the Conservative Party.
She will formally leave office, handing her resignation to the Queen at Buckingham Palace, immediately after the final result is announced.
Her final duties in her job will include welcoming President Trump during his state visit to the UK next month.
The G20 Summit of world leaders in Osaka, Japan, at the end of June is likely to be her swansong on the world diplomatic stage.