May is the only remaining candidate in the Tory leadership race, after Leadsom announced that she would be pulling out of the contest - and gave her backing to the home secretary, whom she said is "ideally placed to implement Brexit". May has also received the backing of previous leadership contenders Michael Gove and Boris Johnson.
Graham Brady MP told reporters that there were constitutional processes, and internal party processes to be followed - but said the selection process would not be re-opened.
While he would not be drawn on how long those processes will take, the chair of the 1922 Committee said May's appointment would not require a meeting, and a "conversation" would suffice.
May was already the frontrunner to win the leadership - she had the backing of 199 Tory MPs against Leadsom's 84 in the most recent party ballot.
David Cameron announced that he would resign as PM after the UK voted to leave the EU last month.
Meanwhile, former shadow business secretary Angela Eagle announced her bid for Labour leadership just minutes before Leadsom dropped her bombshell.