The 27-year-old has been with his current club throughout his career, making his debut in 2003 after graduating through the academy.
Prieto has made over 200 appearances for the Basque outfit, scoring 34 goals, and has been in excellent form this term, helping to guide the club to a mid-table position.
Despite links with a club of the stature of the Reds, the former Spanish under-21 international insisted that he was happy where he was.
"There is nothing to what has been published," he told Spanish newspaper AS.
"Liverpool are a very good team, but I've always said I'm happy here."