Sports newspaper Estadio Deportivo claims that Rafa Benitez is keen on landing the 19-year-old, whose contract at Sevilla expires next month.
There are several clubs reportedly interested in the central midfielder, and Benitez is said to have been keeping tabs on the youngster in recent months.
Formerly of Spanish giants Barcelona, Viedma joined Sevilla in 2016 and has mostly turned out for their second team in the Spanish Segunda Division.
He made four appearances for Sevilla Atletico, and has also turned out for Los Rojiblancos in the UEFA Youth League this season.
Meanwhile at the Stadium of Light, the wheels are in motion as new owner Stewart Donald looks to appoint the Black Cats' next manager with players incomings, and outgoings, expected to be announced once a new man is at the helm.
Here's the rest of the news hitting the headlines today:
Manchester United are keen on a move for Chelsea attacker Willian (Sky Sports)
Robert Lewandowski is a target for Chelsea, with the Blues making the Bayern Munich man their top summer target (Telegraph)
Tottenham youngster Reo Griffiths, 17, is a surprise target for Barcelona (Star)
Spurs could then raid Premier League rivals Manchester United for out-of-favour striker Anthony Martial (London Evening Standard)
Manchester City are poised to sign Riyad Mahrez from Leicester City after narrowly missing out on the Algerian in January (Manchester Evening News)
Fulham boss Slavisa Jokanovic has emerged as a shock contender for the Chelsea job - if Antonio Conte leaves (Express)