The information was reported by news websites Zdopravy.cz and ČT24 reported. Travel Service spokeswoman Vlaďka Dufková declined to comment. Travel Service is expected to issue a statement soon.
Travel Service, which owned 34 percent, has agreed to buy a 44 percent stake from Korean Air and another 19.7 percent from Prisko.
ČSA will have roughly 98 percent after the transaction. Insurance company Česká pojišťovna holds 2.3 percent. ČSA, long in financial trouble, returned to profit in 2016.
Chinese company CEFC holds a 49.92 percent share in Travel Service. The remaining shares of Travel service are held by founder Jiří Šimáně and his business partners.
Travel Service together with Unimex Group previously tried to buy ČSA in 2009. In the end, the government canceled the sale.
Korean Air had bought into Czech Airlines in 2013 but did not exercise an option to increase its stake by another 34 percent. In 2015, Travel Service picked up the stake instead. Many of the investments that Korean Air promised to make in ČSA did not occur, according to daily Mladá fronta Dnes.
Aside from its stake in Czech Airlines, Travel Service also operates charter flights in the Czech Republic, Slovakia and Hungary, and the low-cost carrier Smartwings.
Travel Service was founded in 1998 and owns 31 planes, with 30 on order. ČSA was founded in 1923 and has 18 planes with one on order.
State-run Prisko has originally founded the National Property Fund in the 1990s and was involved in settling debts of state-owned companies.