CHICAGO (From news reports) -- R.R. Donnelley & Sons Co. said a mystery bidder that has been circling the publishing company since at least November has raised its offer again.

The unidentified suitor made another non-binding offer to buy R.R. Donnelley, this time for $11.50 a share in cash, the company said in a statement on Thursday. The buyer had previously offered $11 a share for the Chicago-based business.

The news could upend R.R. Donnelley's agreement to be bought by Chatham Asset Management LLC for $10.85 a share. The board hasn't determined that the new proposal is superior and continues to recommend the Chatham deal. A proxy statement regarding that deal is expected to be filed on Jan. 21, and a shareholder vote is planned for Feb. 23.