The JFA said previously the manager would be foreign and picked from a shortlist of five after Mexican Aguirre was sacked last month because of fears his alleged involvement in a match-fixing case in Spain could hurt the team.
Japan's Kyodo News on Monday quoted Daini as saying he expected the Bosnian to put pen to paper by March 12.
"I think it should be alright," said Daini, who was briefed on the talks by JFA technical director Masahiro Shimoda.
Daini said on Saturday the JFA wanted to finalise the deal at its executive board meeting on March 12.
Japan have friendly matches scheduled against Tunisia on March 27 and Uzbekistan four days later.
The 62-year-old Halilhodzic has extensive club management experience, including stints in France with Lille, Rennes and Paris Saint-Germain.
On the international front, he was at the helm during Ivory Coast's unbeaten run through 2010 World Cup qualifying, and coached surprise package Algeria at the 2014 Cup in Brazil.
Michael Laudrop had also been linked with the Japan job but his contract with Qatar club Lekhwiya runs until July.
(Writing by Peter Rutherford in Seoul; Editing by Amlan Chakraborty)
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