The 18-year-old Spaniard, who will be out of contract at the end of the season, has been linked with Tottenham, West Ham and Fulham as well as Sunderland, who are managed by his father Gus.
A host of scouts were understood to have watched Poyet put in another impressive display in Charlton's 1-0 win over Bournemouth on Tuesday night, and the Addicks face losing him for a nominal compensation fee in June unless he signs a new deal.
"The contract is our business, but be sure we have our eyes very open about it," admitted Addicks boss Jose Riga.
"Diego is still young but the maturity in his game is right.
"In this environment he will always receive good advice and he is happy at the moment. He can be a very good player."