He said the cost of such a trip could be around US$100m, "possibly less for the first tourist".
The tourists will be able to "go out on a spacewalk and make a film, (or) a video clip".
Energia, which was behind the launch of the first man in space Yuri Gagarin in 1961, is currently building a new module dubbed NEM-2 to transport tourists to the International Space Station (ISS).
Solntsev said the NEM-2, the name of which is still to be confirmed, will accommodate four to six people.
It will be fitted with "comfortable" cabins, two toilets and internet access.
"It should be launched in 2019," he said.
"Basically it will be comfortable, as much as that is possible in space," the space official was quoted as saying.
He added that American aircraft manufacturer Boeing was interested in becoming a partner in the project.
Five to six tourists a year will be able to take a space trip lasting up to 10 days, Solntsev said.
Space tourism is a developing sector currently dominated by Western companies, such as the US-based Virgin Galactic, which unveiled its commercial SpaceShipTwo in 2016.
Russia sent Canadian founder of the Cirque du Soleil, Guy Laliberte, into space in 2009.
The billionaire spent two weeks on the ISS.
Iranian-American entrepreneur Anousheh Ansari became the first female space tourist in 2006.
Russia is hoping to welcome space tourists to the International Space Station (ISS) by 2022.
In December, it was revealed that the nation's space agency, Roscosmos, is reviewing plans for a five-star hotel onboard the space station.
The "luxury orbital suite" will feature four private cabins, measuring two cubic metres each, with personal portholes so tourists can look down on Earth.
But a stay won't come cheap. Tourists will be charged £30m ($57.8m) per person for a one to two week visit.
An extended month-long visit will set travelers back an additional £15m.
The luxury hotel will feature a lounge area with a giant 16-inch window, as well as two "hygiene and medical" stations.
It will also boast exercise equipment and even Wi-Fi, according to a proposal seen by Popular Mechanics.
As well as being able to gaze down on Earth from their lofty vantage point 220 miles (350km) miles above Earth, tourists will be offered the opportunity to take part in space walks.
Overall, the habitat will weigh 20-tons, feature a 15.5-meter-long module would provide 92 cubic meters of pressurized space.
The proposed hotel is estimated to cost between £210m and £336m.
Roscosmos says it will be funded by both private and public investments.
Russia's main space station contractor, RKK Energia, wants to book at least 12 passengers who would agree to make payments of around £3m up front.
Currently, the launch of the module is planned for 2021.
RKK Energia estimates that it would take at least five years to build the tourist module, which means that if the work began straight away, it would make it to the station in 2022, according to Popular Mechanics.