The company hopes greater foreign ownership will help speed its restructuring from a state-run bank to a modern financial conglomerate that offers banking, insurance and brokerage products under one roof.
The comments accompanied news of a 24 percent rise in second-quarter profits.
Foreign investors now own 15 percent of First Financial, which became Taiwan's first bank to sell shares overseas last year when it sold $515 million of depository receipts, lowering the government's stake to 25 percent from 32 percent.
"First Financial will increase profits with greater cross-selling synergy and improved products," said Chao Yuan-chi, the financial firm's new president.
"If we can double foreign ownership to 30 percent in two to three years, that would be a sign that we have improved our operations," Chao told a news conference.
Chao said he was more concerned with improving First Financial's operations than merging with another company, a topic of frequent discussion in local newspapers due to overcrowding in the Taiwan banking sector.
Hua Nan Financial Holding has expressed interest in tying up with First Financial, but the two state-controlled firms have put those plans on hold as labour unions oppose the tie-up, fearing job losses.
"Mergers are a long term trend in Taiwan, but I am not thinking about that now," Chao said.