The petition was signed by many but not all of the 134 cardinals present at Monday's meeting, according to the Italian daily Corriere della Sera.
The prelates have clearly caught the popular mood following the funeral Mass for the late Pope last Friday, when some in the massive crowd began chanting 'santo, santo', demanding that the Polish-born pontiff be declared a saint.
The letter had been left on a table for cardinals to sign and at the end of the meeting was handed to the dean of the college of cardinals, Germany's Joseph Ratzinger, who will have the task of delivering it to the next Pope, the newspaper said. Vatican spokesman Joaquin Navarro-Valls said that they had begun "an exchange of ideas on the general situation of the Church in the world and on the Holy See", without giving details.
Archbishop Edward Nowak, the secretary of the Vatican office in charge of declaring saints, was quoted as saying on Monday the Church could put John Paul II on the fast-track to sainthood from as early as October as the next Pope could bypass the usual lengthy procedure.
"The synod of bishops is meeting in Rome in October and it could be an appropriate opportunity to make such a decision," said Archbishop Nowak.
Ordinarily, Church rules decree that five years must pass after death before the question of sainthood is tackled, to allow for cooler assessment of the subject's life, although at least one cardinal is believed to have revived talk of an ancient custom of allowing canonisation by acclamation.
The rush to sainthood gathered pace within days of John Paul II's death on April 2, with a stream of reports of purported miracles carried out in his lifetime reaching Rome. However, only those occurring after his death would count toward his sainthood.
Only three popes have been canonised in recent history: Celestine V in the 13th century, Pius V in the 16th and one of John Paul II's close predecessors, Pius X in the early 20th century.
Meanwhile, in St Peter's Square, special-edition Vatican stamps went on sale. The 'vacant see' stamps mark the period between John Paul's death and the election of his successor, and were being snapped up quickly by collectors.
The Vatican said over three million pilgrims flocked to Rome from April 2-8, 21,000 people entering St Peter's Basilica every hour to see the body of John Paul II.
The Vatican said the longest line reached 5km.