The Spain Under-21 international has been attracting interest from clubs around Europe following his performances in the European Under-21 Championships in Italy.
Oyarzabal scored twice and made an assist in Spain’s victory over Germany in the European Under-21 final to earn a glowing reputation heading into the summer transfer window.
Unsurprisingly, speculation in Spain has suggested that the 22-year-old could leave Real Sociedad this summer to take the next big step in his career.
Former Liverpool FC midfielder Xabi Alonso is currently in charge of Real Sociedad after his appointment earlier this month.
And ex-Real Sociedad star Lopez has now urged Oyarzabal to consider a move to Liverpool FC ahead of the new Premier League season.
Lopez told Marca: “I really rate him. I don’t think he has a lot of time left at Real Sociedad.
“He has so much talent and I think he could play in a great team like Chelsea and Liverpool.”
Oyarzabal has scored 38 times in 151 games since the attacking midfielder made his debut in the 2015-16 season for the Basque club.
The promising midfielder netted 13 times in La Liga last season.
His new Sociedad manager Alonso completed a £14m move to Liverpool FC from Real Sociedad in the 2004 summer transfer window.
The deep-lying midfielder won the Champions League and the FA Cup during his six-year spell at the Anfield side.
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