Pepsi-Cola Co. is negotiating a deal for what could be one of the highest-profile promotions in marketing history: an unprecedented $35 million program that would award the winner a ticket to ride on the Russian Soyuz space shuttle.

Should it reach agreement on buying a seat on the rocket, the soft-drink giant would back the program with a powerhouse marketing budget. Among its plans: a reality TV show with contestants competing to win a trip to space. Executives working on Pepsi-Cola’s behalf are fashioning a program around the concept and are negotiating with at least one undisclosed network, according to a person familiar with the situation.