Ford, 45, went to Humber River Hospital last Wednesday, at which point doctors discovered the tumour. He has since been moved to Mount Sinai Hospital.
The Toronto Sun's Joe Warmington reported Tuesday that the mayor has had a biopsy on his lungs, following an initial biopsy taken last week on the abdominal tumour.
His brother, Doug Ford, says that doctors are expected to update the public on Ford's condition on Wednesday.
While Rob Ford has pulled out of the mayoral race, his name will be on the ballot as a council candidate in Ward 2.
His brother, Doug Ford, is now running for mayor instead. The Oct. 27 municipal election is less than six weeks away.
Rob Ford spent nearly a decade on council before running for mayor in 2010. His brother was elected to council when Ford was elected as mayor.
Ford's term as mayor has been filled with controversy, particularly in the last year and a half during a scandal that saw him admit to using crack cocaine. He eventually entered rehab and returned to work in June after a two-month absence.
The drug-related scandal made headlines around the world and turned Ford into a celebrity. He was mocked by high-profile comedians on late-night TV and even made an appearance on Jimmy Kimmel's show.
Throughout it all, Ford defied calls to step down from office, even though his fellow councillors stripped him of some of his powers in the wake of the drug scandal.