Blatter, who led world football's governing body for 17 years, was suspended from the sport for six years for ethics violations in 2015 amid the biggest corruption scandal to shake FIFA.
Several officials from the body were indicted by U.S. and Swiss authorities, although Blatter himself was not and he denies any misconduct.
The 82-year-old's attendance at the World Cup could put him in close proximity to his successor, Gianni Infantino, who has sought to draw a line under past scandals.
FIFA did not comment when asked about Blatter's plans.
Renggli said the Swiss has not yet decided when he would make his trip to Russia or what game he would attend, but that he would definitely not attend the opening ceremony or inaugural match between Russia and Saudi Arabia on Thursday.
Blatter was at the helm of FIFA when Russia won the right to host the World Cup in 2010, beating England, among others, in its bid.
In 2015, Putin said Blatter deserved a Nobel Prize for his stewardship of football's governing body and that he was sure Blatter was not personally involved in corrupt activity.
Kremlin spokesman Dmitry Peskov said in October both Blatter and ex-UEFA head Michel Platini, who was also suspended following an ethics investigation, would be welcome at the World Cup as "old friends" of the Russian president.
The tournament, which is taking place in 11 cities at 12 venues, will run from Thursday until July 15.
(Writing by Tom Balmforth; Editing by Christian Radnedge)
