Hojiblanca already holds a 10 percent stake in Deoleo, the world leader in sales of bottled olive oil.
"If it's possible, we are not ruling out buying that stake. We are considering it," Antonio Luque said in an interview with El Economista published on Saturday.
Bankia, rescued by the Spanish government last year, must sell stakes in other companies as part of a restructuring plan imposed after Spain received around 40 billion euros ($52.09 billion) of European aid for its ailing financial sector.
Other shareholders in Madrid-based Deoleo are expected to sell their stakes too, Luque said, and Hojiblanca would wait to see how things progress before purchasing Bankia's stake.
Another rescued bank subject to restructuring plans, unlisted lender BMN, has a stake in Deoleo.
Hojiblanca, based in the southern Spanish region of Andalusia, owns 10 percent of Deoleo after Spain's competition body approved the acquisition, subject to Hojiblanca giving up its brand name and a factory in Malaga province.
"What is our strategy for the future? To have a bigger stake in Deoleo," Luque said.
"A total merger is impossible ... Taking a bigger stake in the future, well yes," he added.
Hojiblanca and Deoleo together produce 15 percent of Spain's olive oil and account for 22 percent of sales in the country, according to Luque. ($1 = 0.7679 euros)
