"The final tests for launching the capsule, carrying a monkey, have been completed," Iran's Space Organisation chief Hamid Fazeli said in remarks reported by the Mehr news agency.
Fazeli said the launch would take place during a 10-day period starting January 31, which marks the 34th anniversary of the 1979 Islamic revolution, the state television website reported.
Iran has already sent small animals into space -- a rat, turtles and worms -- but its previous attempt to send a live monkey into space failed in 2011, which was announced without explanation.
Fazeli said the monkey project would help Iran "implement the preparations of sending a man into space," which officials say is scheduled for 2020.
The previous project envisaged launching a capsule with life support using the Kavoshgar-5 rocket to an altitude of 120 kilometres (75 miles) for a 20-minute sub-orbital flight.
Iran says it has successfully launched three satellites -- Omid in February 2009, Rassad in June 2011 and Navid in February 2012.
But it postponed, without explanation, the planned launch in May of another satellite called Fajr.
Iran's space programme deeply unsettles Western nations, which fear it could be used to develop ballistic missiles capable of carrying nuclear warheads they suspect are being developed in secret.
Tehran has repeatedly denied that its nuclear and scientific programmes mask military ambitions.