After a £5.2 million move from Malaga last summer, Ramirez has endured a torrid time in England, with just a single goal in 15 Toffees appearances.
He then failed to score on loan at Sevilla in the second half of last season, but his 16 goals for Málaga the previous year demonstrates the sort of form potential suitors hope the one-time Barcelona forward can replicate.
Ramirez has not featured in a competitive game under new manager Marco Silva this campaign, and while Silva has been impressed with his attitude, he admitted the Spaniard will find it difficult if he stays at Goodison Park.
Speaking to the Liverpool ECHO, Silva said:
“I spoke with Sandro two weeks, three weeks ago, I was clear with him, he was clear with me. He did a good pre-season, he worked hard and took his position in our squad. He is a good professional, a very good professional.
“Of course, when he didn’t perform like he wanted to during his first six months with the club for him it is clear the competition will be tough – but not just for him but the others as well.
“But in my opinion he is ready to fight and ready to compete to take his position in the squad and help the squad to improve as well.
“About if he is leaving or not, I don’t have anything more to talk about.”
A transfer for Ramirez is likely to cost about £9 million, though Everton may also entertain another temporary deal for the striker.
Should a move to Sociedad materialise, it must be finalized before the Spanish transfer deadline on Friday, August 31.