The application, submitted only last week, would mean an upgrade of the west side of the store next to Pakenham Road.
The extension would be built on part of the existing car park, and the car park itself would be extended on to the currently empty piece of triangular land near the back of the store.
Some councillors have expressed concern at what they say might be a "disturbance" and "inconvenience" for residents, while others suggest the store needs to "take a more community- focused view" before planning further extensions.
Cllr Dale Birch, vice-chairman of the borough council's planning and highways committee, said: "We would seriously need to look at the impact on the local area of any expansion.
"At the moment local ward councillors are extremely concerned about the issue of abandoned trolleys, and they are unlikely to give their support to a plan which might exacerbate such problems.
"The superstore needs to take a more community- focused view of the possible adverse impact of any planned extensions."
Cllr Gill Birch, who represents the Birch Hill and Hanworth ward, which is closest to the store, said that "instead of building up and expanding the site, Sainsbury's should first concentrate on dealing with existing problems, and I won't be supporting the application until they do".
The leader of the Labour group, Cllr Austin McCormack, agreed that "there will naturally be concerns", even though "the extended store will provide better services for shoppers".
He added: "The location will be a problem for many residents, and there will be disturbance and inconvenience.
"Where Sainsbury's gain, residents might lose, so this application certainly sets some alarm bells ringing."
A spokesman for Sainsbury's said the store was "keen to hear residents' views" before the application went further.
It will be discussed by the planning and highways committee on July 11.