The Serie A club's scheme, presented by president Edoardo Garrone, included 1,000 car park spaces plus another area that could host other sporting events.
"Experience teaches us when clubs own their stadiums they make more money while also bringing extra benefits to the city," Garrone was quoted as telling the Italian news agency ANSA.
"This is my father's dream for his city and his team," he told La Repubblica newspaper.
Sampdoria want to build the new stadium in the Fiera district on the Genoa seafront but did not say how much the development would cost.
New stadiums have become a major issue for Serie A clubs since champions Juventus moved into their new home at the end of last season and the switch produced an instant increase in attendances.
Inter Milan, Lazio and Roma are also intent on having their own stadiums.
Roma, who ground-share with Lazio, announced plans last year to build a new 55,000-60,000 capacity venue by 2016. Inter also have a ground-share scheme with AC Milan.
Last month Udinese secured a 99-year lease of their council-owned Stadio Friuli venue and the surrounding land.
The club will pay the Udine council 45,000 euros ($59,100) a month and are committed to structural upgrades worth 21.5 million euros.
($1 = 0.7618 euros)