The Dutchman could only muster a third-placed finish with the Blaugrana last term and has seen his side begin the 2021-22 season with eight points from their opening four matches.
Koeman refused to take questions from the media in a recent press conference - instead reading out a statement pleading for support - and Laporta has now admitted his growing frustrations with the 58-year-old.
Speaking to Sport, Laporta said: "We found out at the last minute that he wanted to make a statement and, well, he's obliged to attend press conferences and he's free to respond or speak as he wishes.
"We respect the coach's decision, but we and the captains found out a bit before. We're in a difficult moment and I think that we should have a lot of serenity and wait for a good result tomorrow against Cadiz, because that's what interests us, situations which you overcome with results."
When asked if his patience with Koeman was starting to wear thin, the Barca president simply responded: "Yes, of course."
The Blaugrana now prepare to take on Cadiz in Thursday's La Liga clash on the back of Monday's last-gasp draw with Granada, and the club have supposedly drawn up a five-man shortlist of potential candidates to replace Koeman.
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