Chiquito and Frankie & Benny's in Greenbridge retail park are under threat.
The Restaurant Group, owner of both franchises, has said it will close 88 of its establishments other the next six years with a further 100 also closing in the long term.
The company owns 352 restaurants including Frankie & Benny's, Chiquito, Garfunkel's and Coast to Coast, with half of these expecting to close once their leases expire.
But out of the 352 sites, 15 will be converted into a Wagamama restaurant after the company bought the brand last year.
The group has two stores in Swindon, both at Greenbridge, whilst also having a Wagamama site in the Outlet Village.
It is not yet known if the restaurants, located next to Empire Cinema, will close.
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