Barcelona suffered a shock 1-0 defeat to Valladolid at the weekend and the result has seen them fall to third in La Liga, four points behind league leaders Real Madrid.
The result put Martino’s future in doubt as it was the Catalan club’s second defeat in their last three Liga matches, however Bartomeu hopes the 51-year-old will stay on at least until his contract expires in 2015.
"Martino has a contract with us until June 2015," he told Cadena Ser. "We would like Martino to remain with us next season.
"We hope he will remain with us for a long time. He is eager to do things well and win."
The president also confirmed that Barcelona will look to bring in at least two new players this summer, with replacements for outgoing goalkeeper Victor Valdes and defender Carles Puyol being the priority.
"We have two definite signings," he added. "One is a goalkeeper and the other one is a central defender.
"Over the last year we have looked at a long list of goalkeepers and we have narrowed the selection of those that are more adequate for the position.
"We have spoken to them. The fans can be calm regarding this."