The club said on Monday coach Juan Antonio Pizzi, a group of players and the directors were due to fly to Rome after winning the Inicial, the first of two championships in the 2013/14 season.
Former Buenos Aires archbishop Jorge Mario Bergoglio, anointed pope in March, is an honorary member of the club nicknamed the Saints of Boedo for the barrio where they were founded by a group of young men that included a priest in 1908.
"It's a lightning visit...It's going to be emotional, (the pope) is our number one fan, we're taking the trophy and a championship to him which is no small thing," club general manager and former striker Bernardo Romeo told reporters.
"What happiness," Pope Francis was quoted as saying by Argentine daily La Nacion when he heard of San Lorenzo's 12th title on Sunday.
The pope has been seen receiving shirts and scarves from fans with San Lorenzo's blue and red colours during his public appearances.