The Scottish and English football authorities have resisted any moves towards a Team GB.
However, Lord Prescott, during a heated campaign visit in Rutherglen, suggested a No vote would lead to opportunities for a joint Scotland-England effort.
The former Labour MP for Hull made the call as he delivered a speech where he was repeatedly shouted at and heckled.
He said: “We’re Better Together and it’s something we should tell the Scotland football coach. If England and Scotland were one team we might finally be able to beat Germany.”
He repeatedly told hecklers to “shut up” and was given a police escort to a cafe after he finished speaking in Rutherglen Main Street.
Lord Prescott told Yes supporters they were “shouting down people who disagree with independence” during a bad-tempered exchange.
He added: “Of course there’s a lot to be done, but the leadership has come from Scotland and I’m here as a Welshman, representing a northern constituency most of my life, to argue to keep that character, to keep that contribution that is Scottish.”