Shani, the ministry's director general, was in Italy last week for bargaining sessions with Alenia Aermacchi, which has offered its M-346 Master as a replacement for the Israeli air force's venerable Vietnam War-era Douglas A-4 Skyhawks, which are being retired.
KAI is offering its T-50 Golden Eagle.
Air force sources say the two aircraft were pretty much evenly matched regarding operational capabilities. The deciding factor will be who offers the best deals to sweeten the pot for Israel's defense industry in a global market increasingly driven by export orders as military spending in the United States and Europe shrinks.
The Italians have offered deals with state-owned Israel Aerospace Industries, flagship of Israel's defense sector, worth $ 1 billion. In December, Seoul upped the ante by dangling potential deals worth $5 billion.
The contest has taken some bizarre twists and turns.
At one point, it looked like the T-50 was the front-runner. But then the South Koreans complained Israel had initialed a preliminary agreement with Italy, which if it went ahead was expected to be part of what the Haaretz daily termed "a wide-ranging trade deal" between the two countries.
Amos Harel, one of Israel's leading defense writers, reported in Haaretz that seven months ago Shani had indeed inked a preliminary deal with his Italian counterpart.
"The document, which was formulated according to demands submitted by Israel, expanded the deal beyond its original framework," Harel observed.
Italy reportedly pledged if Israel signed with Alenia Aermacchi, "the two sides would sign additional deals worth more than $1 billion."
These would include joint development of satellite projects, probably involving IAI, and the sale of unmanned aerial vehicles, an Israeli specialty, to Italy.
The Jerusalem Post recently reported that Rome was discussing a possible barter deal under which Italy would get two AWACs aircraft from IAI in exchange for the M-346 deal.
But KAI has come up with a long-term package deal potentially worth $5 billion to persuade the Israelis to go for the T-50.
"KAI alone has offered Israel more than $1 billion in industrial cooperation if its aircraft is chosen," The Jerusalem Post reported recently. "The remaining deals are expected from the South Korean government."
"Potential cooperation could be on the T-50, our helicopters and other programs," the Post quoted Enes Park, KAI's executive vice president for marketing, as saying.
Park also said KAI is having talks with IAI, flagship of Israel's defense sector, and Haifa-based Elbit Systems, one of the world's largest defense electronics manufacturers, about joint ventures that could involve lucrative deals for Israeli companies.
Italy had been seen as a front-runner because of Israeli Prime Minister Binyamin Netanyahu's close relations with Prime Minister Silvia Berlusconi. But Berlusconi's resignation in November, hastened by a slew of political scandals, may have undermined the Italian position regarding the advanced trainer contract.
Italian hopes took another hit Nov. 19 when an M-346 crashed into the Persian Gulf soon after takeoff from Dubai where it had participated in the prestigious air show.
The pilot and co-pilot ejected safely. The cause of the accident hasn't been announced.
Meantime, KAI has garnered considerable support among Israel's defense companies, largely due to the fat contracts Seoul is offering if the T-50 is selected.
Seoul has also indicated that if Israel buys the Italian trainer, all military procurement deals between the Jewish state and South Korea would be scrapped, Israel's media says.
Current defense deals between the two are worth some $280 million a year to Israel.
Seoul has shown keen interest in acquiring the Iron Dome counter-rocket system built by Rafael Advanced Defense Systems.
Israel is keen to export this and other systems such as IAI's mobile high-altitude, anti-ballistic Arrow and the medium-range David's Sling system Rafael is developing.
The South Koreans have also expressed interest in acquiring Israeli unmanned aerial systems, anti-tank missiles, command-and-control centers and upgrades for combat jets.
2014: The Year in Music [PHOTOS]