The Iceland international has been attracting big club interest this summer.
Blazquez told Tuttosport: "There are offers for Albert, but none of them meet our expectations.
"I understand him, I understand his push to leave at the best moment of his career, but for us the most important thing is Genoa. Until we have a solution in hand that makes us feel comfortable, at the same or at a better than last year's level, we cannot sell Albert and, as of today, he will not leave."
On facing Inter on Saturday and the Gudmundsson links, he also said: "These are things you read in the newspapers, we have never had a formal offer from Inter, he is a player in whom there is interest from many teams, so far Fiorentina has made an offer, but we did not consider it acceptable. I think Inter are interested but to date they have not sent us any offers.
"If the offers do not convince us and there is no suitable replacement, we will remain 100% with Albert, we are happy to keep him and he wouldn't be so sorry either."