33-year-old Veloso joined Hellas last year after his Genoa deal expired, helping them to 8th place in Serie A.
According to the local Corriere di Verona newspaper, Veloso has agreed to extend his contract by one year.
His new deal will run until June 30, 2021, with an option to extend it for a further season.
The outline of an agreement in place with Hellas expected to confirm the extension soon.
Veloso has won 56 caps for Portugal, and has played for Sporting, Dynamo Kyiv and Genoa at club level.