Al-Sadr has been strongly opposed to the US presence in Iraq and controls a powerful militia known as al-Mahdi Army.
On Thursday, Turkey's Anatolia news agency cited unnamed diplomatic sources as saying that al-Sadr's visit was aimed at "holding consultations on the political process in Iraq".
He was expected to travel to Istanbul after his talks in Ankara.
Ties have been strained between Ankara and Baghdad over Kurdish fighters based in northern Iraq.
In March, Gul was the first Turkish head of state to visit Iraq in 33 years in an effort to improve relations.
Turkey has made it a foreign policy priority to improve ties with its neighbours and make efforts to ease tensions in the Middle East.
Turkey recently hosted indirect peace talks between Israel and Syria and helped negotiate a ceasefire in Gaza.
Al-Sadr's popularity grew in Iraq in the months after the US-led invasion of 2003. His allies won enough seats in Iraq's January 31 provincial elections to emerge as a key political player.
But he has avoided public appearances since June 2007, giving an interview to Al Jazeera in March 2008 but mostly just issuing statements through senior aides.