They would be introduced from late next month if approved by Scottish Borders Council next Thursday.
Areas to be covered include Coldstream, Galashiels, Hawick, Jedburgh, Lauder, Melrose, Peebles, Selkirk and West Linton.
The zones will be reviewed after a year as part of an 18-month trial.
Speed limits would also be cut from 60mph to 40mph on several roads including the B7062 Peebles to Traquair.
The move come two years after Edinburgh became the largest area of Scotland to complete a scheme for 20mph limits on most streets.
Gordon Edgar, Borders council’s executive member for roads and infrastructure, said: “If approved, the introduction of 20mph areas will be a hugely significant change for all of our communities.
"But it is worth emphasising this is a pilot which will be continually reviewed throughout its duration.”
The trial will be accompanied other measures devised with walking and cycling developers Sustrans Scotland.
Mr Edgar said: “Coronavirus has changed the way we live and move around, and as a result we felt this was the perfect time to work with Sustrans Scotland to try out new measures that may shift the balance towards walking and cycling, which we may not otherwise do.
“This trial will aim to help people in the Borders lead healthier lifestyles, and at same time help reduce CO2 emissions."
Sustrans Scotland director Karen McGregor said: “It’s clear people across Scotland want to do the right thing during coronavirus.
"They want to look after their physical and mental health.
“They also want to make sure that they are keeping to physical distancing guidelines while still being safe on our streets.
“Providing funding support to Scottish Borders Council through our Spaces for People programme will make it easier and safer for Borderers to travel around their area for essential travel and exercise.”
However, a motoring group was unconvinced about the move.
Temporary measures ‘look awful’
Neil Greig, the Scotland-based policy and research director of motoring group IAM RoadSmart, said: “It’s now well established that simply putting up 20mph signs without changing the look and feel of a street doesn’t make cyclists and walkers feel much safer.
"We support high-quality segregated facilities and investment in attractive environmental improvements such as street furniture, planting and new surfaces.
"It is vital Borders Council consult widely on these changes, as far too many of the temporary facilities being seen on our roads look awful and remove much-needed parking spaces as our high streets come back to life.”
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