The veteran midfielder has been a key figure in the Benfica team since joining from Atletico Madrid in 2013.
But with Benfica embarking on a major spending spree this summer, several players will inevitably go.
The Lisbon club are not actively trying to sell Pizzi, 30, but are open to offers of €20m-plus for their number 21.
Pizzi is entering his seventh season at Benfica and has never expressed any desire to leave before.
However, there is a feeling that now may be the right time for the 17-time Portugal international to try a new experience abroad.
Pizzi has made 281 appearances for Benfica, scoring 76 and assisting 86 goals.