The two could sign the deal to develop Block 37 within the next week following a state visit to the Caribbean island nation, Reuters reported.
The news wire cited Yuri Ushakov, an aide to President Vladimir Putin, as saying that he intends to visit Cuba starting on Friday, where it is hoped the companies will sign the agreement with state oil player Cubanpetroleo (Cupet).
In May Rosneft chairman Igor Sechin signed a memorandum of co-operation with Cupet general director Juan Torres Naranjo covering offshore exploration.
Upstream reported in June that Zarubezhneft is now not scheduled to return to Cuban waters to start drilling until next year at the earliest.
Zarubezhneft had originally committed to bringing an offshore rig back to Cuba this year, after stopping work on its prospect on Block L near the Bahama Platform in June 2013.
Cuba hopes to draw additional players to its offshore sector after a string of disappointing results over the past few years.
Reports on Thursday also suggest that Russia is poised to wipe 90%, equating to some $32 billion, off Cuba’s outstanding $35.2 billion debt to the former Soviet Union.