The force is investigating a gathering in the Durham office of Labour MP Mary Foy in April 2021, when most indoor socialising was banned.
Sir Keir was pictured through a window drinking a beer in the MP’s office after a day of campaigning for the local elections in Durham in April 2021.
Ms Rayner was also at the event, dubbed by some as “beergate” in the wake of the Downing Street “partygate” investigation into lockdown breaches.
Both the Labour leader and his deputy have said they will stand down if fined by police over the investigation - but the pair have insisted they are "confident" that no rules were broken.
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Sir Keir has previously said he “put everything on the line” by promising to step down if he receives a fixed penalty notice, and that resigning would be “the right thing to do”.
"I'm absolutely clear that no laws were broken, they were followed at all times," he has said.
At the time of the Durham gathering, non-essential retail and outdoor venues including pub gardens were open, but social distancing rules – which included a ban on indoor mixing between households – remained in place.
Footage of the incident shows the Labour leader holding a beer
But Labour has argued that food was consumed between work events, meaning it was within the rules.
Ms Rayner, who admitted attending the gathering, said: "No rules were broken. Eating during a long day’s work was not against the rules.
"We have a prime minister who has been found to have broken the rules, lied about it and then been fined. If I were issued with a fine, I would do the decent thing and step down."
Earlier this month, Durham Constabulary announced they had reversed an earlier decision that no offence had been committed, after receiving “significant new information”.
On Tuesday, a Labour Party spokesperson said: “Keir Starmer and Angela Rayner have received questionnaires from Durham Constabulary.”
Labour has sought to contrast Sir Keir’s actions with those of Boris Johnson, who has refused to quit after being fined by the Met Police over a gathering in No 10 in June 2020 to mark his 56th birthday.
Labour sources are confident they can prove the Durham event was work-related and that those present were taking a break to eat while working late on preparations for the Hartlepool by-election.