President Trump and his advisers are privately discussing replacing Attorney General Jeff Sessions and are floating possibilities to replace him, including Sen. Ted Cruz, according to a report Monday night.

The Washington Post, citing people familiar with the talks, said Cruz, R-Texas, and former New York City mayor Rudy Giuliani are among the names "being floated" as possible replacements to Sessions.

Giuliani dismissed an earlier report mentioning him as a possible attorney general and told CNN that Sessions "made the right decision under the rules of the Justice Department" to recuse himself from the Russia investigation.

The Post also said one of the considerations Trump is thinking about is how firing Sessions "would play in the conservative media."

It said some associates of the president view firing Sessions as potentially being part of a strategy to fire special counsel Robert Mueller and end his investigation into Russia's election interference, and whether the Trump campaign conspired in the act.

Sessions is under increased scrutiny after Trump told the New York Times last week that he would not have chosen Sessions to be attorney general if he knew Sessions would recuse himself from the Russia investigation. Trump also criticized Sessions for giving "bad answers" during his confirmation hearing about his Russia contacts.

On Monday, Trump piled on, referring to Sessions' status as "beleaguered" in a Twitter post. Sessions has said he intends to remain attorney general.