The Turkish international has signed a five-year contract with Barcelona but will be unable to play until January due to the La Liga champions transfer ban.
“This is a possibility but the final decision must be made by coach Luis Enrique and it must be a purely technical decision,” Bartomeu told RAC 1.
The Barcelona chief did however, underline that the club does not want him to join a side competing in the Champions League.
“It must be a team not playing in the Champions League.”
Barcelona would be reluctant to allow Turan to join a La Liga rival an he is keen on playing in England which could suggest a brief Premier League move if an offer is made.
There has also been talk of a Galatasaray move but it would be unlikely considering the Lions have booked a place in the Champions League group stages.
Turan is currently the most expensive La Liga transfer of the summer after joining Barcelona on a £24 million move from Atletico Madrid.