It is understood at least 15 fines are imminent, The Guardian reported on Monday night. The fines are expected to be slapped on rule breakers as early as Tuesday.
The Metropolitan Police investigation into 12 events held across government was launched in late January.
It came after an internal inquiry led by civil servant Sue Gray passed information to the force.
The Met has not commented and Downing Street has been approached for comment.
Prime Minister Boris Johnson and his government have been battered by reports of staff parties in Downing Street when Covid restrictions were in place.
The policy inquiry, called Operation Hillman, is focusing on 12 gatherings on eight dates to see if Covid regulations were broken.
Johnson is known to have attended at least three of the gatherings.
He has said he did not believe he was breaking any rules, but apologised “for the things we simply didn’t get right”.
The Met said it would contact people “believed to have taken part in the events in question to get their accounts”.
The force had sent questionnaires to dozens of staff members, aides and ministers, including Mr Johnson and Chancellor Rishi Sunak.
Investigators have already been supplied with more than 300 photographs and 500 pages of material, from the inquiry led by Ms Gray.
Ministers backed Johnson not to be issued with a penalty by police.
Oliver Dowden, the Tory co-chair, told LBC: “The prime minister is actually absolutely resolutely clear that he is not going to be subject to a fixed-penalty notice because he is confident that he has not broken the law.”