The 31-year-old, who will be a free agent in 2014, recently said that he would not be signing a new contract at Camp Nou.
However, the shot-stopper may have to wait until his deal expires before he is allowed to leave Barca.
"As we prioritise sporting aspects, we prefer to run out the contract until June 2014 rather than sell him this summer," The Mirror quotes Bartomeu as saying.
"We have no deadline in Valdes's case, one option is to run to the end of his contract and in that case we will not sign a goalkeeper [this summer]."
Arsenal are one of a number of clubs linked with a summer move for Valdes.