The midfielder was a target for the Black Cats during the January transfer window but they couldn't get a deal over the line.
Sunderland reportedly made a bid of around £15m for the Greece international in the final days of the window, but it was rejected by Benfica as they could not find a replacement.
And now, according to A Bola, the Portuguese club are ready to end talk of Samaris leaving by offering him a new contract.
The 27-year-old's current deal expires in June 2019, but the fresh terms on the table would extend that until the summer of 2021.