Epsom and Ewell Borough Council’s environment and safe communities committee will meet on Wednesday to discuss the plans.
Five pitches could be approved for the station end of Stoneleigh Broadway, where stalls could trade seven days a week.
In Ewell Village, the market could set up in The Grove, which is the alleyway between Ewell Village High Street to West Street.
The plans said markets and street traders could increase footfall to an area, which would help speed up economic recovery and give local businesses the best chance of survival after the pandemic.