Rose, which says it was the first independent marketing agency to launch in the Soviet Union in 1989, has joined firms such as WPP and Llorente & Cuenca in targeting the communist state.
It follows a thawing of relations with the US, which is set to end its five-decade-old embargo on Cuba.
In a statement, Rose said it planned to be among the first marketing firms to launch its services in Havana, where it hoped to expand into a full-service PR, advertising, media and marketing services group.
No timescale has been given for opening in the country, but Rose said the plan was to launch with a "well-trained Cuban team" under Rose general director Galina Savina.
Rose said it had already begun working in Havana as it did in Moscow: "by installing a representative to explore opportunities, establishing a local team, advising its clients on how best to enter the market, making business introductions and developing localised marketing programmes".
A spokeswoman said a local team is being assembled in Cuba, initially involving three or four people. "The legal structure of the agency is in process and should be completed early next year together."
She said Rose is in discussion with "several international and Cuban companies regarding representation". "Rose is primarily targeting international brands, joint ventures and distributors (as it has done in Russia) and a few large Cuban enterprises that have requested consultation."
The agency said: "Cuba currently has little to no advertising or public relations and so far prohibits mass media from accepting ads. However, marketing is becoming more important to Cuban state enterprises, international joint ventures and to the new, fast-growing private sector businesses. Rose plans to use its first-mover strategy to ensure it is positioned to grow as the Cuban market for its services takes off."
Savina said Rose began one of the first PR agencies in Russia. "To the extent the government permits us, we will do the same in Cuba," she stated.
"It is inevitable that Cuba’s leaders will lower barriers to marketing communications because it is essential to economic growth in a competitive marketplace."
The agency plans to run Cuba’s first Marketing & Media Summit in Havana in the first half of 2016.
Rose was founded in Boston, US, in 1984 but moved its operations to the Soviet Union five years later amid the collapse of communism. The firm has worked with major brands and companies including Coca-Cola, Citibank, Gillette, GlaxoSmithKline, Logitech, P&G, Samsung, Starbucks, Tourism Malaysia and Volvo.
Rose faces competition from Western firms that are making steps in Cuba or looking seriously at the possibilities.
In July, WPP-owned Burson-Marsteller announced it had launched a service for clients that are planning to enter the Cuban market. Writing in The Daily Telegraph, WPP chief executive Sir Martin Sorrell said: "WPP’s Man in Havana is now in place."
Also that month, José Antonio Llorente, president of Spanish-owned agency Llorente & Cuenca, told PRWeek he planned to open an office in Cuba following a €6.4m ($7.1m, £4.6m) capital injection.
This article was updated on Sunday with additional information from Rose Marketing.