Suarez is believed to be Barcelona's number one transfer target this summer and the fact the player has been banned from playing football for four months by FIFA for his bite on Chiellini has not deterred the club from pursuing his signature.
Suarez, who initially denied biting Chiellini, apologised to the Italy defender via social media on Monday, but did not mention Liverpool in his statement, prompting speculation he is indeed looking to leave the Merseyside club for Barcelona.
It has been suggested that Barcelona encouraged Suarez to apologise for his actions, and Zubizarreta welcomed the move.
"Suarez has shown he is humble enough to admit an error, which is very important," he told reporters.
"He has been humble enough to apologise to those he has affected, because it happened in the middle of a festival of football. In this case it's the best thing a person can do."
The former Barca and Spain goalkeeper also highlighted Suarez's footballing qualities.
"Everyone knows that Luis is an excellent player, everyone knows last season he played in various positions in attack, but everyone also knows that he is a Liverpool player," he said.
Zubizarreta was speaking at the presentation of Barcelona's latest signing Ivan Rakitic, and the midfielder also praised Suarez.
"The fact he has had the character and the strength to go in front of everyone and say sorry says a lot about him as a person," said the Croatian international.
"Not every person has that strength to admit they have done something stupid. I rarely say that I am wrong so this says a lot about him, he has shown the character and strength he has so he should be commended for that.
"Regardless of whether the club signs him or not, his quality is unquestionable. He has shown a lot of quality with Uruguay and scored more than 30 goals (last season) with Liverpool, so he has the necessary quality to play for Barca."
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