The Daily Star previously claimed that United manager Louis van Gaal was looking at the England international as a potential transfer target following his blistering start to the new campaign.
However, Schmeichel - whose son Kasper plays alongside Vardy at the King Power Stadium - has claimed that the Dutchman would be better off looking elsewhere, but has admitted that the striker should certainly be leading the line for the national side.
"I don't think he would fit in," he is quoted as saying by the Daily Star. "I'd love to see Jamie Vardy move on and become stronger and play for England and start for England, but even that is a debate.
"This is the top scorer in England in the Premier League. He has just beaten this incredible record.
"He has just beaten Ruud van Nistelrooy, who is an unbelievable goalscorer and you are having the debate of should he play for England?"
The Great Dane's assessment comes shortly after Vardy broke Ruud van Nistelrooy's record by scoring in an 11th consecutive game, when he broke the deadlock against the Red Devils, which makes the suggestion slightly perplexing.
Having spent much of his career in the non-league game, the 28-year-old has proved that he has the ability to find the back of the net at any level, and thus, making the step-up to United - although it is the Foxes who are above van Gaal's men in the table currently - may not be beyond him.
His presence may well inject the kind of pace and energy that United fans have been crying out for this season.
United have adopted a methodical style under Van Gaal, and it could be Vardy's arrival that elevates them further.