Health Minister Jeremy Hunt said on Sunday May had asked officials to investigate if Garnier, whose role is outside the Cabinet immediately surrounding May, had broken the government ministers' code of behaviour.
"These stories, if they are true, are obviously totally unacceptable," Hunt told BBC television.
"The Cabinet Office will be conducting an investigation as to whether there has been a breach of the ministerial code in this particular case, but as you know the facts are disputed."
May will also write to John Bercow, the Speaker of the House of Commons, to ask for his advice about changing the culture there, Hunt said.
Reports of inappropriate behaviour in British politics, and in other industries, have followed dozens of allegations against Hollywood producer Harvey Weinstein. Weinstein has denied having non-consensual sex with anyone.
