Source: Sharecast
Following meetings with the Communication Workers Union in recent weeks, a deal is expected to be announced on Monday morning, the BBC said.
The deal had been under scrutiny under the National Security and Investment Act as Royal Mail's operations are considered vital national infrastructure.
Kretinsky has already offered several guarantees in a bid to secure the deal, including promises to maintain the "one price goes anywhere" universal service and not to raid the pension surplus.
He has also said he will keep the brand name and Royal Mail's headquarters and tax residency in the UK for the next five years and respect union demands for no compulsory redundancies to take place until 2025.
The government will retain the right to approve any major changes to Royal Mail's ownership, HQ location and tax residency in the future.