The cardinal did his teaching practice at an RC grammar school in north London, and is believed to have stayed at an RC presbytery, rather than in student accommodation.
Percy Evans was his tutor on the PGCEcourse that focused on education in tropical areas. which the cardinal attended in 1963.
Mr Evans told The TES: "He had a lovely sense of humour and was always laughing. He was very nice, very meetable - which will come in handy.
"If he is successful, I will write to him and congratulate him."
Cardinal Arinze, who is Nigerian, is one of the top five papal candidates and on the conservative wing of the church.
In February, he said pro-abortion Roman Catholic politicians should not be allowed to take Holy Communion, while people who act upon homosexual tendencies would be condemned by the Church.
In 2003, the cardinal angered some staff and students at Georgetown university in the United States, when he said: "In many parts of the world, the family is under siege. It is opposed by an anti-life mentality as is seen in contraception, abortion, infanticide, and euthanasia. It is scorned and banalised by pornography, desecrated by fornication and adultery, mocked by homosexuality, sabotaged by irregular unions and cut in two by divorce."