The 41-year-old, who has been in charge of the Middle Eastern outfit since 2019, has been heavily linked with replacing the Catalan club's current manager Ronald Koeman, who is at risk of losing his job.
Xavi is believed to be on a five-man managerial shortlist drawn up by Barca, along with Roberto Martinez, Jordi Cruijff, Andrea Pirlo and Antonio Conte.
The former Spain international has enjoyed a successful spell in charge of Al-Sadd, winning one league title as well as five other domestic trophies, and in October he is set to lead out his side in the Emir Cup final, facing Laurent Blanc's Al Rayyan.
Despite this upcoming fixture, Marca reports that Al-Sadd would not stand in the way of Barcelona if they decide to enquire about Xavi's availability and would allow him to return to Camp Nou.
The report also states, however, that Xavi is not prepared to enter negotiations with Barca while Koeman is still in charge, as he does not want to 'betray' the Dutchman who he considers to be a club icon.
Xavi made 767 appearances in all competitions across a trophy-laden 17-year career with Barcelona, winning 19 domestic titles as well as lifting the Champions League on four occasions.