Eliseu is to leave Malaga for Benfica for a €1m fee, according to reports from Spain.
Marca says the move has come as a surprise as the 30-year-old had only recently signed a new deal with Los Boquerones.
But he is now travelled to Portugal to discuss terms with the Lisbon club while Malaga have ventured to Australia for a pre-season tour.
Eliseu had been criticised by Coach Javi Gracia for being overweight and his new Malaga contract was said to be based on appearances.
The Portugal international is in line for a three-year contract at Estadio da Luz, according to Cadena Ser.