The Spanish international is expected to be out for four to six weeks, leaving Liverpool light on midfield options with Alex Oxlade-Chamberlain and Curtis Jones also sidelined.
Midfield was already arguably the weakest area of a Liverpool squad that came within two games of winning an unprecedented quadruple of trophies last season.
But Klopp said the club would already have added in that area if they thought it necessary.
"I am happy with the strength, size and quality of my squad. We have injuries. Now it is the question how long the players will be out and there are different solutions," Klopp said on Friday at his pre-match press conference for Monday's clash with Crystal Palace.
"One - and there are plenty - is the transfer market but the transfer market only makes sense if you can bring in the right player, not a player.
"If there was the right solution out there then we would already have done it. We're not stubborn and say 'no way, we don't bring in anybody'.
"If there would be the right player we would have done it, we would do it, but I don't see it because we had a lot of conversations already and it doesn't look like something will happen."
Klopp turned to 36-year-old James Milner off the bench to inject some life into the Liverpool midfield in a disappointing 2-2 draw at newly-promoted Fulham to start their Premier League campaign last weekend.
Afterwards, Klopp was scathing about his side's performance, claiming they were lucky to escape Craven Cottage with a point after twice coming from behind.
He is expecting a far faster start for Liverpool's return to Anfield for the first time this season on Monday.
"I didn't like the start at all. I saw then the attitude to fight back but that's a different thing. It's better you have a high intense, high concentrated, lively start in a football game than not," added Klopp.
"Having a slow start doesn't mean you have to start slow all the time or you will never do it again, but it's a sign. Use it as information, change it and go from there."
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