(Reuters) - Books-A-Million Inc said the Anderson family, which includes Chairman Clyde Anderson, on Saturday made a non-binding proposal to take the company private.

The Anderson family, which already has a 53 percent stake in the book retailer, is offering $3.05 per share in cash for Books-A-Million -- a premium of 20 percent to Friday's closing, the company said.

The offer values Books-A-Million at about $48.8 million.

Last month, the company replaced Clyde Anderson with Terrance Finley as its new chief executive and reported a higher fourth-quarter profit.

Anderson stated he anticipates the acquisition would be in the form of a merger of Books-A-Million with a newly formed acquisition vehicle that the Anderson family would control.

The chairman also stated in the letter that the transaction would be financed through borrowings available under the Books-A-Million's existing credit line, and is conditioned on availability of sufficient funds under the credit line.

Anderson said he expects that the Board will establish a special committee of independent directors to review the proposal and the family will not move forward with the deal unless the committee makes a favorable recommendation.

Shares of the Birmingham, Alabama-based company closed at $2.55 on Friday on the Nasdaq.

(Reporting by Chris Jonathan Peters in Bangalore; Editing by Sreejiraj Eluvangal)