Messi penned a two-year extension to his existing deal with Barca last February, which ties him to the club until June 30, 2018, but the Spanish champions are ready to discuss a new contract with the 26-year-old.
Bartomeu, who took over the Barca presidency on Thursday night following Sandro Rosell's shock resignation, also warned potential suitors that Messi is not on the market amid reports of interest from big-spending French side Paris Saint-Germain.
Speaking to Catalan radio station RAC1, Bartomeu said: "Messi is not for sale.
"We want to sit down, without any rush, with his father and his agent because we want to ensure he's the best-paid player like he deserves.
"It won't be anything imminent because the players right now are focused on competition."
Messi made his 400th appearance for Barca in last week's Copa del Rey quarter-final first leg against Levante and has scored 331 goals so far for the Catalan giants.
During his time at the Nou Camp, Messi has won the Ballon d'Or a record four times as well as helping Barca win a host of trophies, including six Primera Division titles, three Champions Leagues and two Copa del Reys.