The Dutchman signed a two-year deal with the Brazilian side in June after opting not to extend his stay at AC Milan, but Roberto Carlos has made it clear that he could have made a move to Russia.
"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," the former Real Madrid star stated to reporters.
"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."
The 36-year-old Seedorf is the only player to have won the Champions League with three different clubs.