Slovenia, which fully owns the bank, pledged to sell 75 percent of NLB by the end of 2017, but put the sale plan on hold last June.
It said the expected price, which would value the whole bank at a minimum of 1.1 billion euros (£962 million), was too low.
The government, which injected 1.55 billion euros into NLB in 2013 to prevent it from collapsing under a large amount of bad loans, notified the Commission of a set of new commitments in December.
Its proposals consist of an extension of the deadline for the sale until 2019 as well as the appointment of an independent trustee to oversee shareholders rights in the meantime.
"At this stage, the Commission has doubts whether the new Slovenian proposal can be considered equivalent to Slovenia's original commitment," the Commission, which oversees competition policy in the European Union, said.
Slovenia's finance ministry said in a statement on Friday that it plans to lead "a very intensive dialogue" with the European Commission before it officially replies to the Commission in a month.
"The key goals of the government in the continuous talks remain keeping a controlling stake of 25 percent ...in NLB, pursuing privatisation in line with market conditions that will enable maximum return of taxpayers money invested in the bank in 2013 and enabling the bank to remain an important regional financial institution," the ministry said.
On Thursday, Finance Minister Mateja Vranicar Erman told reporters she did not expect the European Commission to order NLB to return the state aid.
(Reporting by Robert-Jan Bartunek, additional reporting by Marja Novak in Ljubljana; editing by Philip Blenkinsop and Jason Neely)
