The 25-year-old - also linked with Arsenal, Barcelona and Bayern Munich - was identified as a leading target for the Merseyside giants in the number six role after his rise to prominence in his homeland.
Zubimendi had already affirmed several weeks ago that he had no intention of leaving Sociedad, but he appeared to briefly have a change of heart when it emerged that Liverpool were working on a deal to sign him.
Sociedad had supposedly resigned themselves to losing the Euro 2024 winner to Liverpool, but the two clubs never agreed a fee, as the Spanish giants insisted that his €60m (£51.1m) release clause be paid in full.
As Liverpool tried to put together a suitable payment structure, Zubimendi was caught in two minds over leaving his boyhood club, and he eventually decided to snub the Reds and stay put with Sociedad.
Slot confirms Liverpool interest in Zubimendi
With the 25-year-old remaining in La Liga, Liverpool head to Ipswich Town for Saturday's Premier League opener as the only English top-flight team not to have made a single signing this summer.
Speaking to the media in his pre-game press conference, Slot confirmed that Zubimendi turned down a move to Anfield, but the Dutchman does not believe that his squad requires serious improvement.
"I've said many times already that I think our squad is really strong, and it's not so easy to find players that can help us or can even strengthen the squad," Slot said. "Zubimendi was one of them to be fair, but he decided not to come.
"We go forward with the ones we have, and [Wataru] Endo's one of the ones who's done really well in pre-season, so we're in a good place. On the background, Richard [Hughes] is trying to strengthen the squad as he can, but unfortunately Zubimendi decided not to come. He did every effort, he tried everything to bring him in but if a player doesn't want to come, it's obvious that he is not coming."
In addition to Zubimendi, Slot was also questioned on the future of Colombian winger Luis Diaz, who has been at the centre of intense transfer speculation despite his status as a fundamental player for the Reds.
Slot: 'Diaz's future is with Liverpool'
The former Porto man has been heavily linked with a move to Barcelona this summer, and there was also short-lived talk of interest from Manchester City, which was quickly shot down.
Diaz has not signed a contract renewal since joining in January 2022, but Slot has insisted that his future is on Merseyside, adding: "There's a lot of speculation in this country, so it's not a surprise if I hear you saying about Luis Diaz.
"His future is with us, because I like a lot what I have seen in the last 10 days, and I saw the same last season, so he's had a big impact on Liverpool seasons, and I'm hoping that he has a big impact on this season as well."
Diaz scored twice in a 4-1 friendly win over Sevilla last weekend, and the 27-year-old is expected to start at Portman Road on Saturday afternoon in Slot's first competitive match at the Liverpool helm.
The Dutchman also confirmed that he has every member of his squad fit and available for the weekend, while Mohamed Salah, Virgil van Dijk and Trent Alexander-Arnold will all be involved despite the uncertainty surrounding their contract situations.