“I am conscious that the Conservative Party wants to have someone who they believe is very enthusiastic about Brexit,” she said.
“There are all sorts of plans I would like to have when we do leave the European Union but I don’t think it is my time at the moment.”
Ms Rudd did not say who she would back in the June leadership contest, but hinted at a future working relationship with Mr Johnson.
Speculation has mounted in recent weeks that the Hastings and Rye MP could back Mr Johnson in a leadership race.
The former foreign secretary is widely considered the frontrunner to replace Ms May.
Ms Rudd did not formally back Mr Johnson when asked but said she got on well with the former foreign secretary.
“Sure, I like him yeah. To be brutal I like most of my colleagues,” she said.
“I am not somebody who actually fights. I get on perfectly well with him.”
“I have worked with him before,” she added.
“He was Foreign Secretary, I was Home Secretary. We were able to work together.”
The politician has not always praised Mr Johnson.
In 2016, while debating him about leaving the EU, she remarked that she would not like him to drive her home.
She has also called the former foreign secretary “untrustworthy” and labelled his Brexit stance “pure fantasy".
The Conservative leadership race will formally begin on 10 June, three days after Ms May steps down.
Additional reporting by agencies