The club's current home at the 11,450-capacity Vitality Stadium is leased from property company Structadene.
Chief executive Neill Blake said the club would "not be held to ransom" over a price to purchase the ground or "develop a ground they do not own".
Bournemouth, in their second top-flight season, hope to have a new stadium built in time for the 2020-21 season.
"We feel we have no other option but to find a new site," Blake added. "We are working closely with Bournemouth Borough Council to identify a suitable location."
The Cherries have played at their current ground, formerly known as Dean Court, since 1910, but it was sold to Structadene in 2005 in a sale-and-leaseback deal.
The council has previously stated it would not welcome a "significantly bigger stadium" in the Kings Park area of the town.
Its chief executive Bill Cotton said it will do "all it can to help the club in their search for potential sites".
A planning application to expand the ground's South Stand, increasing capacity by 3,000, is due to go before the council's planning committee in January.
Premier League club AFC Bournemouth have confirmed they intend to build a new stadium in a new location.