Subway founder Fred DeLuca is keeping America’s second-biggest restaurant chain in the family.

The Milford, Conn.-based sandwich chain said on Thursday that DeLuca’s sister, Suzanne Greco, had been promoted to president and would take over day-to-day operations.

DeLuca will remain CEO and will continue to help set Subway’s strategic direction, the company said.

DeLuca has been battling leukemia for more than two years, and there has been speculation he was interested in selling Subway for some $6 billion, or taking the chain public.

DeLuca said Thursday, “Suzanne has accomplished a great deal with Subway, and I know there are more terrific things to come.”

The Post reported exclusively in February that DeLuca, 67, had essentially given control over to Greco, 57, even though she was only senior vice president.

She takes over at a critical time, as Subway, like rival McDonald’s, suffers same-store sale declines.

In 2012, the average Subway restaurant generated $482,000 in annual sales. That fell last year to $460,000, according to John Gordon at Pacific Management Consulting Group.