The national season is currently suspended indefinitely, with cancellation of the campaign a real possibility.
Liverpool need only two more wins to end their 30-year wait for the championship title, while United pursues the top four and is still involved in two cup competitions.
But Shaw believes United rivals should not be awarded the title if they cannot complete their remaining matches.
Asked how to handle such a situation, Shaw said in a FIFA Combat Corona Twitch competition: “Give it up and try again. Try again, yes. It must be you know. If we cannot continue, it must be nil. “
Premier League leaders still hope to end the current season and are working hard to configure plans for a proposed restart.
They held talks with the British government on the potential prospect of returning to action in June.
It would depend entirely on the peak of the epidemic, and the league leaders continue to play with the idea of playing matches behind closed doors.
Shaw added, “Fans are so important. You realize it even more [now]. I think sport is really for the fans, you know what I mean? I think if you don’t have fans and you don’t play in front of fans, that doesn’t seem fair to you.
“Especially on the day of the match, the fans are always amazing and always help the team. Whether at home or even outside, our fans are always brilliant and I have the impression that they are always there with us. “
UEFA chief Aleksander Ceferin has also admitted that the Champions League and Europa League competitions could be canceled if they cannot be completed by September.
Coronavirus in sport
Both competitions are suspended until further notice, with a four-team tournament scheduled for July or August.
“We can’t play in September or October,” Ceferin told ZDF Sportstudio.
When asked if the season could be dropped, he added, “If the authorities don’t allow us to play, we can’t play. “