The sources say Trump was deeply disappointed by Sessions' decision, which he viewed as a sign of weakness, though the president rejected the AG's offer to resign.
Earlier Tuesday, White House press secretary Sean Spicer said he could not answer when asked if Trump still has confidence in Sessions.
"I have not had that discussion with him", Spicer said.
Sessions' offer to resign was first reported by ABC News.
An administration official told CNN that Trump's frustration with Sessions dates back to March 2, when Sessions suddenly recused himself from the Russian Federation investigation amid pressure from Democrats on Capitol Hill. Sessions selected Deputy Attorney General Rod Rosenstein to head the investigation, which Trump believes ultimately resulted in the appointment of special prosecutor Robert Mueller.
Rubin: Israelis pleased, over all, with Trump visit
Trump visited the Western Wall in a private capacity and was not accompanied by any Israeli leaders. "There's a new guy in the White House", Estrin said.
Minnesota Joins State Alliance To Uphold Paris Accord
Elected officials and private sector leaders across the USA plan to defy President Donald Trump's position on climate change. Virginia is one of 13 states and territories that are committed to upholding the Paris Climate Agreement .
Kim bests Nordqvist to claim ShopRite LPGA
According to LPGA projections, Ko's reign will end after the ShopRite Classic with either Ryu or No.2 Ariya taking over. This was Kim's first LPGA win in the United States since 2009, for her two previous wins had come in Mexico and China .
Sessions remains at the Justice Department, where a spokeswoman told CNN that he is not stepping down.
In May, the Justice Department appointed Muller as special prosecutor for the alleged Russian interference in the U.S. election, a decision which Trump called "the single greatest witch hunt in history".
Trump's anger over the recusal has not diminished with time.
On Monday morning, Trump took aim at the Justice Department on Twitter for its defense of his controversial travel ban on six Muslim countries, which is now blocked by the courts. "If I haven't had a discussion with him about a subject, I tend not to speak of it". The ban and a second version written to better withstand legal scrutiny have been held up in court.
President Donald Trump and Attorney General Jeff Sessions have had a series of heated exchanges in the last several weeks after Sessions recused himself from the Russian Federation probe, a source close to Sessions told CNN Tuesday. That recusal is connected "in some way" to "much of the past two months of discomfort and self-inflicted pain for Trump", the Times wrote.