The Washington Post first reported these negotiations, which according to two officials are not going over well with Republicans.
Senate Republicans are proposing some $25 billion in grants to states for testing and contact tracing, as well as about $10 billion for the CDC and $15 billion for the NIH, the sources said.
A senior White House official told ABC News, "the President is fully committed to a robust aid package that addresses real needs" and said "there have really been no negotiations to date."
The official did not directly dispute that the administration is seeking to zero out funding for contact tracing and testing, arguing that health experts even say it will never work, but said it's early in the negotiating process and talks will start in earnest Monday.
"There have really been no negotiations to date. There have been a couple of conversations about current funding needs and reserves from the previous legislative packages," the official said. "The President is fully committed to a robust aid package that addresses real needs. There remains 14.7 billion dollars in NIH and CDC from the previous cares act allocations and discussions will start in earnest on Monday."
This news comes days after public health officials and lawmakers sounded alarms over a new program that directs hospitals to report COVID-19 data directly to the Department of Health and Human Services instead of to the CDC.
While the White House says the new requirement, which started Wednesday, will help make coronavirus data collection from hospitals more centralized and efficient, some fear HHS control and using a system run by a private contractor instead of existing CDC data collection channels could politicize findings and cut experts out of the loop.
The White House on Friday also blocked CDC Director Robert Redfield from testifying before Congress next week on how to reopen schools safely
Congress is now racing to put together the next coronavirus stimulus package before lawmakers break for the August recess, tentatively scheduled to begin Aug. 10, and unemployment benefits -- desperately needed by so many Americans -- run out at the end of the month.
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Senate Majority Leader Mitch McConnell is poised to introduce his bill this week as he prepares to sit down with Democrats to negotiate the next stimulus package before the November presidential election.
Two senior GOP aides said the Republican bill will come in at roughly $1 trillion to $1.3 trillion.
House Speaker Nancy Pelosi derided that sum as far too little, pointing to her chamber's passage of a more than $3 trillion coronavirus relief bill two months ago. It included $75 billion for testing, contact tracing and isolation measures.
"I have no doubt they will come around," Peolsi said in a Bloomberg interview. "In the beginning they said, 'No, we have spent enough money.' Now, they're at $1.3 trillion. That's not enough. We have $3.4 trillion."
McConnell has knocked the bill as a "liberal wishlist."
The two sides remain far apart in several key areas.
Democrats have insisted on the House-passed bill that includes aid for front-line workers, state and local governments, and more money for hospitals, testing, schools, nutrition and housing assistance. Senate Democrats are seeking to add an additional $430 billion for education-related needs. Thursday, Senate Democratic Leader Chuck Schumer and his caucus also unveiled a $350 billion plan to target aid to communities of color, which have been disproportionately hit by the coronavirus.
Outlining his bill Thursday, McConnell said four key themes will prevail: liability protection, schools, jobs and health care.
As the nation's unemployment rate remains historically high, it seems certain lawmakers will continue expanded pandemic jobless benefits. But Congress is unlikely to continue those benefits before they run out at the end of this month.
Republicans have fought against a flat $600-per-week rate created under the original CARES Act virus relief bill, claiming it is a disincentive to work for those who made less before the virus hit. Senate Finance Committee Chairman Chuck Grassley, who would manage that portion of the bill, has indicated that the benefit is likely to taper off and not end abruptly.
There is a lingering question about whether or not to send Americans of modest income another round of stimulus checks, one of the more popular provisions of the last stimulus bill. Trump has expressed support, and Sen. Roy Blunt, R-Mo., said Thursday he was "open to it."
The one area where there is far more agreement is aid to small businesses. The popular Paycheck Protection Program, which was renewed until Aug. 8, is likely to be reformed to target the smallest of businesses. Many businesses have requested a chance to apply for a second PPP loan, but it is unclear if Republicans will approve such a move as it would swell the overall price tag of the bill.
McConnell said on Thursday he knows the path forward will not be an easy one.
Unveiling his plan mid-week "will just begin the process," he said.
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ABC News' Katherine Faulders, Mariam Khan, Libby Cathey, Anne Flaherty and Jordyn Phelps contributed to this report.