Liverpool mayor Joe Anderson says resuming the Premier League is a "non-starter", and he fears a "farcical" situation with fans congregating outside Anfield - even if Liverpool clinch the title at a neutral venue.
The Premier League has told its clubs only "approved venues" will be used, raising the possibility of matches being played at neutral grounds.
Liverpool, chasing their first title for 30 years, lead the table by 25 points with nine games remaining, while the league hopes to restart on 8 June.
The league's "Project Restart" envisages the season resuming behind closed doors because of social distancing measures in place to battle the coronavirus pandemic.
Liverpool say they are "disappointed" with Anderson's comments.
The national lead for football policing said on Wednesday that playing all remaining Premier League and EFL fixtures at their original venues would "present challenges" to the emergency services.
Deputy chief constable Mark Roberts said "options" need to be looked at.
Anderson, Liverpool's first directly elected mayor, told BBC Sport: "Even if it was behind closed doors, there'd be many thousands of people who would turn up outside Anfield.
"There's not many people who would respect what we were saying and stay away from the ground, a lot of people would come to celebrate so I think it's a non-starter."
Asked about whether playing at a neutral venue would help, he said: "Even then, I guess that a lot of people would turn up outside Anfield to celebrate and I understand the police's concerns around that, so there's a real difficulty here for us.
"I think it would be really difficult for the police to keep people apart and maintain social distancing if they were going to celebrate outside Anfield. It would be farcical.
"It's difficult for us to try to stop people gathering in parks when the weather has been good, especially young people. And I fear people would just ignore it.
"The police are right to be concerned about that as we are here in the city, and public health officials are also concerned about that, so we'd ask the Premier League and government to take into account all of these concerns that we have."
In a statement, Liverpool said: "As well as a lack of evidence to support such claims, we would also point to recent discussions with mayor Anderson relating to the possibility of any behind-closed-doors football, which concluded that it is important that key stakeholders across the city continue to engage and work collaboratively.
"In recent weeks, we have engaged with supporters' groups who have informed us of their determination to respect social distancing measures and, in the event of a resumption of football being announced, we would continue to work with them and other key stakeholders in keeping with our collective desire to achieve this crucial objective.
"As part of our ongoing operations, we are in regular contact with the mayor and his office and we hope these conversations can continue."
'Liverpool should be champions - but end the season'
Anderson added: "I think the best thing to do is to actually end the season.
"It isn't just about Liverpool - they've clearly won the league - they deserve it, they should be crowned league champions.
"The bottom line is, though, this is about health and safety and people's lives and I think football should have to come second in regards to making a choice here."
More than 300 people have died from coronavirus in Liverpool hospitals.
The Premier League will hold a meeting on Friday morning when Project Restart will be discussed.
Meanwhile, the senior medical directors of the FA, Premier League, Rugby Football Union, England and Wales Cricket Board and the British Horse Racing Authority will also hold talks on Friday in the first of a series of meetings to discuss the feasibility of a return to play.
Culture Secretary Oliver Dowden, England's deputy chief medical officer Jonathan Van-Tam, UK Sport CEO Sally Munday and a representative of the Sports Ground Safety Authority will also be on the call.
BBC Sport has learned that sports leaders will be asked to give evidence to MPs at a Department for Digital, Culture, Media & Sport select committee hearing on Tuesday on the impact of the crisis on sport.