The game in which Liverpool could secure the Premier League title could be held at a neutral venue, says the national lead for football policing.
Deputy Chief Constable Mark Roberts says up to six matches could be moved at the request of local police forces.
They include the Merseyside derby as well as Manchester City v Liverpool.
Roberts said discussions with the Premier League had been "positive" with a "shared focus on the priority of public health".
The Premier League is set to restart on 17 June, subject to government approval.
The fixtures set to be moved to neutral venues are:
- Manchester City v Liverpool
- Manchester City v Newcastle
- Manchester United v Sheffield United
- Newcastle v Liverpool
- Everton v Liverpool
- The game in which Liverpool could secure the title
"We have reached a consensus that balances the needs of football, while also minimising the demand on policing," said Roberts.
"The majority of remaining matches will be played, at home and away as scheduled, with a small number of fixtures taking place at neutral venues, which, contrary to some reports, have yet to be agreed.
"This plan will be kept continually under review to ensure public health and safety and a key part of this is for supporters to continue to respect the social distancing guidelines, and not to attend or gather outside the stadiums."
Liverpool, chasing their first title for 30 years, lead the Premier League table by 25 points with nine games remaining, and Jurgen Klopp's side could win the title against local rivals Everton.
Merseyside Police says that "in relation to crime and disorder" it has "no objections" to the game being played at Goodison Park, and that it would be "ready to provide whatever policing is required of us".
However, Assistant Chief Constable Rob Carden added: "Decisions in relation to public health risk are made by the Government and Public Health England.
"Ultimately the final decision rests with the Safety Advisory Group, which is chaired by Liverpool City Council in line with the decisions made nationally in relation to sporting events."
The Premier League said its "ambition is to complete all of our remaining fixtures this season home and away, where possible".
It added: "We are working with our clubs to ensure risks are assessed and minimised, while co-operating with the police at a local and national level.
"Discussions with the National Police Chiefs' Council and UK Football Policing Unit have been positive and are continuing. We are prepared for all outcomes and have a neutral venue contingency."