The State Emergency Service has issued flood watch and act warnings for the dams at Basket Range and Hope Forest, with road closures in place and local residents doorknocked about the ongoing danger.
Nearby homes could be flooded if the dams fail.
SES chief of staff Derren Halleday said structural engineers had inspected both dams to gauge their integrity.
"As well as the engineer reports, we have personnel physically on-site monitoring and inspecting the dams and their immediate surrounds and we are also working closely with the Department for Environment and Water,'' he said.
Drone footage of the dams is also being used to determine any emergency response.
Mr Halleday said continual rain in the past few days had raised the risk profile of both dams.
There were no weather warnings in place for Adelaide or the hills on Monday, though showers were forecast to continue for most of the week.
The Bureau of Meteorology said flooding was also possible in the northwest and northeast pastoral districts with a ridge of high pressure bringing heavy rainfall.
"This widespread, unseasonal rainfall is likely to begin from Monday in northwestern South Australia," the bureau said.
"From Tuesday this is likely to intensify and start to move more eastwards.
"Heavy rainfall across the flood watch area may cause areas of ponding and overland flow, along with rises in local creeks and overbank flooding."
The bureau said flooding could affect roads and transport, possibly cutting off some communities.
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