Archbishop of Glasgow Philip Tartaglia, Scotland's most senior Catholic cleric, has written to the pontiff asking him to consider a one-day visit to the city in March on the feast day of the saint.
The letter has been written "without any expectations or sense of entitlement" and comes only four years after Benedict XVI made a papal visit to Scotland, with a Mass held in Glasgow's Bellahouston Park.
If Pope Francis does visit, the expectation is that it would be a markedly different, less formal event than Benedict's visit or that of John Paul II, who came to Scotland in 1982.
Notably, St John Ogilvie was a Jesuit, the order to which Francis famously belongs. And unlike his predecessors, the Pope has been closely involved with the church in Scotland, appointing half of the current hierarchy in just over a year.
He has also intervened in the wake of the sex scandal surrounding Cardinal Keith O'Brien and there is an acknowledgement it would galvanise the Church's attempts to move on from the episode.
Church sources discounted any relevance to the proposed visit occurring after the independence referendum. But it would be seen as a clear gesture towards the perception of aggressively secular political agendas.
One senior Church source said: "It's simply a case if you don't ask, you don't get. He's a much more spontaneous and unpredictable Pope than his predecessors.
"He appears to make decisions on visits at short notice and without the usual pomp and ceremony. And he talks about going to frontiers, which for many in the Catholic world Scotland is."
John Ogilvie was a convert to Catholicism and became a martyr for his faith. He was hanged in Glasgow on March 10 1615 and was made a saint by Pope Paul VI in Rome in October 1976.
Archbishop Tartaglia was present at the ceremony as a young priest and he hopes the 400th anniversary will be a "celebration and renewal of faith".
The Archbishop wrote: "It would be wonderful if you could come to Glasgow for a day for this unique event. I would envisage your visit as being of a purely religious-pastoral nature.
"I know that this is short notice for the visit of a Pope. I present this request to you without any expectations or sense of entitlement. I do not even know if it is practical! However, a visit would be such a grace."
Born in 1579, John Ogilvie was raised as a Calvinist and was received into the Catholic faith aged 17 in 1596.
He was ordained a Jesuit priest in Paris in 1610 and returned to Scotland, which was largely Protestant following the Reformation and break with the Papacy in 1560.
While in Scotland, Ogilvie was arrested. Following torture and a trial he was convicted of high treason.
He had been denying the king's spiritual jurisdiction by upholding the Pope's spiritual primacy as well as conducting Mass in secret.
He was hanged at Glasgow Cross on 10 March 1615, aged 36.
Archbishop Tartaglia said: "Whether the Pope is able to come or not, I would hope that the anniversary will be a celebration and renewal of faith for the Catholic community, for other Christians, and for all people of faith."