Muallem is due to hold talks with his Iranian counterpart Mohammad Javad Zarif on Wednesday.
Prior to that, Muallem and Bogdanov will hold a meeting in the Iranian capital on Tuesday night.
The Russian official earlier on Tuesday met with Iranian Deputy Foreign Minister for Arab and African Affairs Hossein Amir Abdollahian in Tehran, and conferred on various issues including terrorism and extremism.
Last year, Iran proposed a four-part plan for finding a political solution to the ongoing crisis in Syria, which was welcomed by the UN.
Iranian officials have since held numerous diplomatic talks with various regional players including Syria and Russia to end the four-year war, started in March 2011. Some 250,000 people have been killed and 8 million homeless during the four-year crisis.