In an interview with Hill.TV, Mr Trump renewed criticism of Mr Sessions' decision to step aside from the inquiry into alleged Russian interference in the 2016 election.
He also said he was unhappy with Mr Sessions' response to immigration.
The attorney general is yet to respond to Mr Trump's comments.
It is unusual for a sitting president to attack their attorney general and critics accuse Mr Trump of trying to meddle in the legal system.
After the president criticised Mr Sessions last month, two key Republican senators signalled that they would support Mr Trump if he were to fire Mr Sessions after the November mid-term elections.
However, other Republicans told Politico they thought this would be a bad move and said they were standing by the attorney general.
Mr Sessions has pushed back against previous criticism by Mr Trump. "While I am attorney general, the actions of the Department of Justice will not be improperly influenced by political considerations," he said in August.
"I demand the highest standards, and where they are not met, I take action."
Mr Sessions was an early supporter of Mr Trump's presidential campaign.
But he left the Russia investigation - which is also reportedly now looking into whether Mr Trump has attempted to obstruct justice - in 2017, citing a potential conflict of interest, and handed control to his deputy, Rod Rosenstein.
The president insists there was no collusion between his campaign and the Russian government, and denies he has attempted to obstruct justice.
What has Mr Trump said this time?
"I don't have an attorney general. It's very sad," Mr Trump said during Tuesday's interview.
He added that he was "very disappointed" about Mr Sessions' decision to leave the investigation.
Asked whether he would consider firing Mr Sessions, the president responded: "We'll see what happens. A lot of people have asked me to do that.
"And I guess I study history, and I say I just want to leave things alone, but it was very unfair what he did [in recusing himself from the Russia investigation]."
Mr Trump also told Hill.TV that he was "not happy" with Mr Sessions on immigration and other issues, and said the attorney general had performed "very poorly" during the nomination process for the post.
"I mean, he was mixed up and confused, and people that worked with him for, you know, a long time in the Senate were not nice to him, but he was giving very confusing answers," he said.
"Answers that should have been easily answered. And that was a rough time for him."
A remarkable attack
By Anthony Zurcher, BBC News, Washington
Donald Trump no longer likes Jeff Sessions, one of his earliest, most prominent supporters. This is not news. There are also political reasons why the president has been unwilling to straight-up fire his attorney general. This is also not news.
That Mr Trump went so far as to say he doesn't have an attorney general - a slightly tamer version of "he's dead to me" - is dramatic, but it's variations on a theme.
What might be surprising, and might also be significant, is the president's decision to criticise Mr Sessions for more than just his recusal from the Russia probe. He doesn't like the way he's handling the immigration issue, for instance.
Given that Mr Sessions was considered to be one of the hardest of the hard-liners on immigration while in the US Senate and the man who helped refine Mr Trump's anti-immigration strategy during the campaign, this is remarkable.
It could also possibly be the beginning of the president's efforts to make a larger case for getting rid of Mr Sessions - after the mid-term elections removes the possibility of immediate political fallout, of course.
If the president can frame axing Mr Sessions as part of a larger political disagreement, that could help deflect some of the intense criticism he will receive for the move.
It's still going to be a rough ride, and confirming a replacement for the attorney general in the Senate will be a monumental task, but the pieces are being moved on the board.