Barkley, who has been linked with possible transfers to Chelsea or Manchester City, has 18 months remaining on his current deal and British media reports suggest no contract talks are planned until the end of the season.
"Football is a business, you make decisions. He (Barkley) needs to sign a new contract or you sell the player," Koeman told reporters on Thursday.
The 23-year-old, who came through the ranks at Everton, has scored five goals in 29 appearances this season and Koeman stressed that he has not offered an ultimatum to the player.
"I think the player needs to understand this. It's not an ultimatum but I spoke to Ross about a new contract and it's up to the board to get that over the line," Koeman added.
"If not, then the player could see a new future for himself, but that is normal. It's not strange talk."
Earlier this week Romelu Lukaku rejected a new long-term deal from Everton that would have made him the best-paid player in the club's history, according to British media, questioning the seventh-placed Premier League side's ambition.
Koeman said he was far from pleased with Lukaku's comments but would not drop the Belgian striker, who is the league's joint-top scorer with 19 goals so far, for Saturday's match against third-bottom Hull City.
Read the full article on eurosport.co.uk: Everton's Koeman hints at Barkley sale