Tests for bacteria in the water supply at RHC have now been extended to four wards at the neighbouring Queen Elizabeth University Hospital, according to NHS Greater Glasgow and Clyde (NHSGGC).
Infection control measures have also been imposed for patients with low immunity.
NHSGGC said it is working with experts from Health Protection Scotland, Health Facilities Scotland and Scottish Water.
A source told BBC Scotland that taps and showers had been taped up in QEUH wards and only bottled water was allowed.
An NHSGGC spokesman said: "These bacteria can pose a risk to patients whose immunity is compromised, however we have put in place robust infection control measures to protect our patients.
"We have now extended this testing and infection control measures to four wards treating the most immunity compromised patients in the Queen Elizabeth University Hospital to ensure that we take every precaution."