Prime Minister Binali Yildirim is expected to attend the meeting, the source, who spoke on condition of anonymity due to restrictions on talking to the media, added.
Bahceli has already congratulated Erdogan over his victory in Sunday's elections.
The MHP and the Justice and Development (AK) Party had participated in the elections together under an alliance.
The two leaders last met on April 18 before the elections at the presidential complex.
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