Al-Ittihad president Anmar Al-Haili admitted that Lionel Messi turned down a billion-plus euro offer last year.
The Argentine international opted to sign for Inter Miami following the end of his deal at Paris Saint-Germain, despite lucrative offers from the Saudis.
Al-Haili said: "We made him an offer of €1.4bn. But he refused because his family wanted to go to the United States. I was surprised, I didn't believe a player could refuse such a big offer for the sake of his family.
"We respect him, because family is more important than money."
Messi is set to lead World Champions Argentina at the upcoming 2024 Copa America that will take place in the United States later this month.