The 69-year-old, who heads Italy's largest toy manufacturer, established Genoa in Serie A during his turbulent 14-year reign but has also twice been banned for misconduct.
With the Griffins on a dismal run and down to 16th in Serie A, Preziosi has faced protests from the supporters in the last two months.
"I confirm that I am determined to sell Genoa, I am ready to hand it over to advisors as soon as we have mathematically ensured our Serie A safety," he said in a statement published by the club.
"Now, those who think I should leave Genoa must make a constructive effort: propose a concrete name, an investor who has the strength to start a new era.
"Anyone who can truly match what we have achieved should step forward and maybe they will be capable of doing even better."
Preziosi took over the presidency in 2003 with Genoa in Serie B.
The club won promotion to Serie A in 2005 but were immediately relegated to the third tier after the Italian league found evidence of match-fixing.
Preziosi was banned for five years although this was later over-turned on appeal.
Genoa finally reached the top flight in 2007 although Preziosi was given another five-year ban, this time for irregularities in financial dealings with his former club Como, which was also later annulled.
"I'm proud of having guaranteed the oldest team in Italian football the position it deserves, a difficult goal to achieve in modern football," said Preziosi.
"It's now been 10 years that Genoa are where they deserve to be in Serie A."
He said he achieved "something nobody else had managed in the post-War period, not even when the city was a strategic centre of Italian and European economy."
(Writing by Brian Homewood; editing by Sudipto Ganguly)
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