"I believe it is a matter of a couple of weeks," the source said, adding that new "May decrees" by Russian President Vladimir Putin may appear when the new cabinet is formed.
The source said the issue of the new government was not raised at Putin's meeting with the outgoing cabinet.
Putin is taking office for a new presidential term later on Monday. After the inauguration, the cabinet will resign.
Late on Sunday, Putin gathered in the Kremlin Members of the Government and thanked them for their work. According to the president, the Cabinet of Ministers has worked with dignity, and this is the great merit of Prime Minister Dmitry Medvedev.