Appointing a second special counsel would be seen as a move to appease President Donald Trump, who has always been critical of Sessions and recently publicly aired his frustrations with the traditional divide between the White House and the Justice Department and his inability to aim the nation's premier law enforcement agency at his political adversaries.
The Post cited a letter it said it obtained from Assistant Attorney General Stephen E. Boyd to House Judiciary Committee Chairman Robert W. Goodlatte, who twice has requested Sessions appoint a special counsel.
Goodlatte also wants a special counsel to look into former FBI Director James Comey's actions directing leaks of conversations he had with President Donald Trump.
Attorney General Jeff Sessions is considering appointing a special counsel to investigate the Clinton Foundation, an Obama-era uranium deal with a Russian company and other issues concerning to Republicans, according to a letter.
Democrats have accused Republicans of launching a spurious investigation of Clinton, the 2016 Democratic presidential candidate, to divert attention from Special Counsel Robert Mueller's investigation into alleged links between President Donald Trump's presidential campaign and Russian Federation.
"Hopefully they are doing something and at some point, maybe we are going to all have it out", Trump said.
Sen. Patrick Leahy, D-Vt., right, talks with Jeff Sessions, who was then a senator and is now attorney general.
In apparent anticipation of those concerns, Boyd said in the letter that Justice Department "will never evaluate any matter except on the facts and the law".
While the Justice Department is part of the executive branch - and the attorney general is appointed by and answers to the president - the White House generally provides input on broad policy goals and does not weigh in on criminal probes.
Last month, Republican leaders of two House committees launched an investigation into an Obama-era deal in which a Russian company bought a Canadian firm that owned some 20 percent of USA uranium supplies.
Justice Department spokeswoman Sarah Isgur Flores declined to comment Monday. Goodlatte and other House Republicans had sent letters to the Justice Department in July and September featuring a wide-ranging list of 14 allegations against Democrats that Republicans wanted investigated.
He struck a similar note before the Senate Judiciary Committee last month, when he denied knowledge of communications between Russians and Trump campaign officials.
What is the Uranium One scandal? That issue has been at the forefront of each of his congressional hearings even as Sessions has labored to promote the Justice Department's work and priorities, and Tuesday's appearance is unlikely to be an exception.