The club official revealed that the Argentine has expressed a desire to return to his first professional team, but made it clear that a move could prove complicated
The midfielder spent last season on loan at Roma, but failed to convince the Giallorossi board to retain him on a permanent basis.
With Juan Roman Riquelme set to depart Boca, the club are believed to be looking to inject more quality in the centre of the pitch, and have pinpointed Gago as a target.
The Argentine outfit tried to sign the 26-year-old last year, but could not iron out an agreement with the Spanish champions over the financial terms of the deal.
However, Crespi revealed that a transfer might take place this summer.
"He wants to come back, and there is a chance. If we don't at least ask Real Madrid about him, we would be fools. We must at least do that," he told Fox Sports.
"He could come here on a reduced salary. In fact he was on the point of coming earlier but the former president [Jorge Amor Ameal] said that he wanted him on a free transfer and the Spaniards went crazy.
"Who doesn't want Gago back at Boca? It would be a great solution."