In his solitary season in the dugout the former Alaves defender lead the Basque club to their first King's Cup final and a ninth-place finish in their first campaign back in La Liga for a decade.
Pellegrino, who has also coached Valencia and Argentine sides Independiente and Estudiantes de La Plata and worked as Rafael Benitez's assistant at Liverpool and Inter Milan, gave no clues about his future, although he denied reports he was leaving for personal reasons.
"I don't have any personal or family problems fortunately and I have felt very happy here as a coach, unlike in other places," Pellegrino told a news conference on Monday.
Alaves missed out on a first trophy in their 96-year history when they lost the King's Cup final 3-1 to Barcelona on Saturday, although Pellegrino said he believed the club had a bright future ahead of it.
"We completed our objectives, and I think Alaves have the right structure, the right experience and the ideal people to continue competing at the highest level," he added.
(Reporting by Richard Martin; Editing by Hugh Lawson)
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