Goal exclusively revealed on Saturday that Arsene Wenger was lining up a £32 million bid for the Chile star following talks with a mystery forward in May.
Manchester City have since joined the race for Sanchez's signature - with Manchester United and Liverpool also linked - and Zubizarreta is keen to find the "best solution" ahead of an expected sale.
"Regarding Alexis, there have been offers. We will try and find a solution best for everyone," Zubizarreta told reporters.
Elsewhere, a host of clubs have been linked with a move for Xavi and the arrival of Ivan Rakitic from Sevilla has raised more questions over the playmaker's future.
Speaking at a press conference to introduce Rakitic as a Barca player, Zubizarreta revealed that he does not know whether Xavi will prolong his stay at the club and plans to hold talks with the midfielder.
"We are talking permanently with Xavi, we spoke to him before he went to the World Cup. He also wants the time to think, that's Xavi Hernandez, he's got every right to analyse things as he wants to do,” Zubizarreta said.
"He's our player, when he comes back from his holidays we'll sit down and we'll talk again. Any news he gives us will be good.
"If he decides to stay that will be fantastic news, if he decides that it might be the time to retire then we will treat that as well as we can.
"We are not talking any old player, we're talking about somebody who is very special. We've been very open with Xavi in our conversations recently, we've been very transparent about things.
"If Xavi stays here he'll be competing with others for a place in the team, but if Xavi decides to explore other options we will respect that."