INA is 45 percent owned by Croatia, with MOL holding a 49 percent stake, and the two sides have been at odds for years over management rights and investment policy at the Croatian oil company.
Croatia said in December last year that it had decided to buy back INA shares and Hungary's Prime Minister Viktor Orban confirmed last month that MOL was ready to sell.
"We're forwarding an invitation to find an adviser that would help the government decide on the best way to buy back INA shares or to find another strategic partner," Crotia's Prime Minister, Andrej Plenkovic, told a cabinet session on Wednesday.
Finance Minister Zdravko Maric told the cabinet that the invitation would be sent to 18 internationally renowned advisers but that others could also bid for the job.
"The deadline for submitting bids is Jan. 15," Maric said.
One of the most important issues will be to determine the value of the transaction.
INA has a market capitalisation of about 33 billion Croatian kuna ($5.14 billion), but analysts have questioned the relevance of the figure given the small free float.