The SNP’s Chris Stephens jokingly proposed the “alternative” idea given Westminster’s refusal to allow a second referendum.
After he noted that football had been raised by several MPs during a Commons debate, Mr Stephens went on to praise Scotland for reaching Euro 2020.
It comes after Scotland beat Serbia 5-4 on penalties to qualify for the tournament.
However, the Tartan Army failed to progress from their group despite a 0-0 draw with England.
Mr Stephens, MP for Glasgow South West, told the Commons: “There are constitutional debates and some people seem to suggest there is deadlock between those who support Scottish independence and those who don’t – and the fact the Government seems unwilling to grant us a referendum.
“Well, I have an alternative idea: if they’re not willing to give us a referendum, perhaps they could give us a penalty shoot-out to decide the issue.
“We know Scotland’s record at penalty shoot-outs is rather good – we managed to qualify for the Euros winning a penalty shoot-out – and there’s England’s record, which is perhaps somewhat different.
“Let’s not sugar-coat it – it’s as poor as the trains going to and from Southend that we regularly hear from (Sir David Amess, Conservative MP for Southend West).”
England reached the Euro 2020 final but lost 3-2 on penalties to Italy after the scores were level at 1-1 after extra time.
Mr Stephens criticised some UK Government ministers for engaging in a “culture war” with the England football team, adding: “I think it’s hard not to like this particular England football team.
“I think they’re a credit to themselves and a credit to England, and I think some of the racism that England players got after the finals was completely and utterly despicable and should be condemned by every single member of this House.”
In response, the Government’s deputy chief whip Stuart Andrew said: “I have to say to him that when he talks about the independence referendum, we gave the people of Scotland a choice. These are not my words: it was a ‘once-in-a-generation opportunity’. They took it, and they decided it was better to stay in the United Kingdom.”