The preparations are the clearest indication yet that Mueller is nearly done with his almost two-year investigation.
The precise timing of the announcement is subject to change.
The scope and contours of what Barr will send to Congress remain unclear. Also unclear is how long it will take Justice officials to prepare what will be submitted to lawmakers.
But with President Donald Trump soon to travel overseas for a summit with North Korean leader Kim Jong Un, Justice officials are mindful of not interfering with the White House's diplomatic efforts, which could impact the timing.
The Justice Department and the special counsel's office declined to comment.
Barr has said that he wants to be as "transparent" as possible with Congress and the public, "consistent with the rules and the law."
Under the special counsel regulations, Mueller must submit a "confidential" report to the attorney general at the conclusion of his work, but the rules don't require it to be shared with Congress, or by extension, the public. And, as Barr has made clear, the Justice Department generally guards against publicizing "derogatory" information about uncharged individuals.
As a result, one of the most pressing questions Barr will face in the coming weeks is the extent to which Mueller's findings should be disclosed to Congress.
The regulations require Mueller to explain in his report all decisions to prosecute or not prosecute matters under scrutiny. Barr would also need to inform Congress if the Justice Department prevented the special counsel team from pursuing any investigative steps.
Trump said Wednesday that it's "totally up to Bill Barr" as to whether Mueller's report comes out while he is overseas in Vietnam next week.
"That'll be totally up to the new attorney general. He's a tremendous man, a tremendous person, who really respects this country and respects the Justice Department, so that'll be totally up to him," Trump told reporters in the White House.
Speculation about the end of the probe has been running rampant in Washington. NBC News reported recently the probe would be done by mid-February.