Deputy chief constable Mark Roberts says "options" need to be looked at.
The league is hopeful of a potential 8 June restart and finishing at the end of July to fit in with Uefa's European competition plans.
Premier League clubs are set to discuss next steps during a video conference call on Friday.
"Playing all those fixtures (in the original venues) would present challenges, that's an bad lot of people moving around the country, and certainly if they were all played at the originally planned stadiums then I think that does present some challenges".
"There's common sense and I think any group of football fans can probably highlight now the fixtures that are probably likely to generate attention".
It is believed that club captains have been told to inform their teammates that the season may now not be concluded with testing of the Coronavirus appearing to be one of the major stumbling blocks.
"There might be a fair deal that if people start gathering and causing public health or public order issues then that might mean that games can't actually go on".
The Premier League has told its clubs only "approved venues" will be used, raising the possibility of matches being played at neutral grounds.
France's GDP contracts to an unprecedented 5.8 percent since 1949
Confirmed US COVID-19 infections have topped one million, according to a Johns Hopkins University tally. Business investment was also weak: It sank 2.6%, with investment in equipment down a sharp 15.2%.
Arsenal were the first Premier League club to open their doors to resume training, albeit under strict social distancing, and further clubs have followed.
"Players at the lower levels will want to go and play because they'll recognise that the alternative is bad - 1,400 players are out of contract in three months so they'll need football to resume so their livelihoods can continue".
"It's not a case of us imposing anything on (the football authorities) or telling them (what to do)", Roberts added.
We're hearing different things every day, but I think if this was a non-economic decision, there would be no football for months.
While talk of players striking if they are asked to return to play is premature, ESPN has approached the Professional Footballers' Association for comment regarding their plans to support those who do not wish to return.
"It is important (to bring it back)".
This would see teams in the automatic promotion places gain promotion but there would be no relegations and for the next campaign there may be more teams to be relegated to once again get the numbers in each division back to normal.