Last week Alan Johnson popped into the the Future Leaders’ Institute in New York. Despite its name and location (in Harlem, near Bill Clinton’s office) this is not a secret training ground for potential British prime ministers or deputy leaders of the Labour party. (“Oops, that never even occurred to me,” says Johnson, his face crestfallen when he realises the irony.) In fact it is a high-performing school for poor pupils.

Founded seven years ago, it is a beacon school in a rundown area, semi-independent of the local education system, and its pupils are subjected to a rigorous regime: lots of targets, sitting straight on wooden benches and extracurricular activities. It is one of the US “charter” schools that Johnson has come to learn from on his first international tour since becoming education secretary in May.

As he whizzed from New York to Washington and then on to Toronto, the heat has been on Johnson to declare whether or not he will stand against Gordon Brown for leadership of the Labour party. But in the bar of his hotel in Toronto where we meet, Johnson is as chilled as the glass of champagne that he sips. Unruffled, he tells me that he is “comfortable” with the position he is in.

This ambitious former postman came to public notice during the kerfuffle over John Prescott’s game of croquet at Dorneywood. While Prezza indulged in toff pursuits, Johnson propped up his working-class credentials by reminding us that he used to deliver letters to the mansion. It was the perfect opener for his campaign to become deputy prime minister — or even PM.

Until now Johnson has refused to speak about his ambitions for the top job. Not that he is confirming his intention to stand — just yet. But he makes it clear that he is giving serious consideration to running. He is beginning to build a popular following and not just with MPs in the ABB (Anyone But Brown) brigade.

A YouGov poll last week suggested that he was by far the most popular senior Labour figure who has been suggested as a potential candidate. Earlier this month, after making a speech to the Social Market Foundation outlining his vision as the “real Labour” candidate, who will do more to eradicate poverty than the chancellor, Johnson was asked whether he would go for it. Silent, he blushed. Why?

“I do blush, I can’t do anything about blushing,” he says, admitting that he was in a “quandary” over whether to answer the question honestly. What would he have said if he could? His answer is carefully worded, but tantalising.

“We now know that the position of leader will become vacant by this time next year. The election for that position is something the party will determine when the prime minister decides he wants to go, and I think Tony deserves the right to choose that date,” he says.

Brown is “the clear favourite” for whom he has “huge admiration”; but he notes that the chancellor has said that he would “welcome” a contest. Not quite the “I’m backing Gordon” endorsement given by other cabinet ministers.

Johnson clearly does consider himself in the running but he will not officially confirm it just yet. He is too shrewd for that. (Although he has already registered the website names Johnson4leader.com, Johnson4leader.org and Johnson4leader.co.uk.)

“My priority is to get on with the job of education secretary,” he says, using the formula trotted out by other possibles when asked about their ambitions. “The public would like us to focus on their futures rather than our own.”

In other words, it is time to stop obsessing about the leadership. Well, of course, a contender would not want to rock the boat too much on the eve of the party conference in Manchester — maybe only a gentle push, anyway.

Despite his coyness in public, there is no doubt that Johnson is giving serious consideration to challenging the chancellor.