The former Arsenal star has been touted as a replacement for wantaway Reds midfielder Javier Mascherano, who has been linked with a move to Inter Milan.
New Anfield supremo Roy Hodgson is thought to be keen on signing Gilberto, 33, who won the Premier League and two FA Cups during a six-year stay with the Gunners.
But the Brazilian's representative, Frank Trimboli, insists his client is not thinking about a move. He said: "Gilberto is very happy in Greece.
"He always wants to play at the highest level and Panathinaikos can offer him the chance to play in the Champions League."