Jurgen Klopp's side faced the Spanish club in a second-leg last 16 tie at Anfield on March 11 in front of a crowd of some 52,000, with 3,000 visiting supporters in attendance.
The match was the last major football fixture played in England before the coronavirus lockdown.
According to the Sunday Times, Edge Health, which analyses data for Britain's National Health Service, estimated the match was "linked to 41 additional deaths" at nearby hospitals between 25 and 35 days later, compared with similar hospital trusts that were used as a control.
Imperial College London and Oxford University have estimated Spain had around 640,000 positive coronavirus cases at the time that the match went ahead compared to 100,000 in Britain at that stage.
March also saw jump horse racing's four-day Cheltenham Festival in southwest England go ahead as scheduled, with officials citing British government guidance that it was safe to proceed with major sporting events.
According to the Edge Health research estimates cited by the Sunday Times, that decision may have been linked to 37 additional deaths.
More than 250,000 people attended Cheltenham, with organisers insisting they had introduced special hygiene measures for the event, including extra hand-washing stations for spectators.
But racing in Britain was suspended on March 17 in response to the pandemic after the British Horseracing Authority was widely criticised for allowing the festival to go ahead.
Last month one of the mayors for Liverpool called for an investigation into why the Atletico match was allowed to proceed as scheduled.
"If people have contracted coronavirus as a direct result of a sporting event that we believe shouldn't have taken place, well that is scandalous," Steve Rotheram, Mayor of Liverpool City Region, told the BBC.
"That needs to be investigated to find out whether some of those infections are due directly to the Atletico fans. There were coronavirus hot cities, and Madrid was one of those." Atletico won the game 3-2 after extra-time to knock out the defending champions 4-2 on aggregate and reach the quarter-finals.
An initial ban on spectators is expected when sport resumes in Britain, which has already seen more than 36,000 deaths during the pandemic -- the worst tally in Europe and second only to the United States.