Seedorf was available on a free transfer after deciding not to extend his stay at AC Milan.
The Dutchman instead signed a two-year contract with Brazilian side Botafogo.
“Seedorf rejected our offer. I talked with him three weeks ago. I asked him whether he wanted to join Anzhi, even though we have a policy not to sign players over 30,” Roberto Carlos said.
“I spoke with him, but he told me that he had already made the decision to sign for Botafogo. I wish him all the best in Brazil.”