Looks like the billion dollar TD Garden site has found its supermarket.

Citing anonymous sources, the Boston Business Journal reports that site owners Boston Properties and the Delaware North Cos. are on the verge of signing Star Market to a 45,000-square-foot lease within the week.

A supplemental filing with the Boston Redevelopment Authority states that the TD Garden owners have reached “a preliminary business agreement with a major supermarket operator,” the BBJ reports. Official details are expected to be made public shortly.

Star Market would occupy the lower level of the 1.7-million-square-foot-mixed-use development, poised to include a 500-unit, 45-story residential tower, a 20-story hotel, a 25-story office building and as much as 376,000 square feet of retail space.

The BBJ reports that Boston Properties has targeted the BRA board’s final session with Mayor Tom Menino next week as an approval date.

Star Market is operated by Shaw’s Supermarkets.