Angelo Scola
Nationality: Italian
Age: 83
Only cardinals under 80 can vote in the conclave, but Angelo Scola could still be elected.
The former Archbishop of Milan was a frontrunner in 2013 when Francis was chosen, but he is thought to have fallen victim to the adage of entering the conclave as Pope and leaving as cardinal.
His name has resurfaced ahead of the conclave, because of a book he is publishing this week on old age. The book features a preface written by Pope Francis shortly before he was admitted to hospital in which he said "death is not the end of everything, but the beginning of something".
Francis' words show genuine affection for Scola, but the college of cardinals might not see his focus on old age as ideal for a new pope.
Marc Ouellet
Nationality: Canadian
Age: 80
Cardinal Ouellet has twice before been seen as a potential candidate for Pope, in 2005 and 2013.
For years he ran the Vatican's Dicastery for Bishops, which chooses candidates for the episcopate around the world, so he has played a significant and formative role in vetting the future members of the Catholic hierarchy.
As another octogenarian, he will not be able to play a part in the conclave itself, which may hinder his chances.
Ouellet is viewed as a conservative with a modern outlook, who is strongly in favour of maintaining the principle of celibacy for priests.
He opposes the ordination of women priests, but he has called for a greater role for women in running the Catholic Church, saying that "Christ is male, the Church is feminine".