Ties between the United States and Turkey - which has the second largest army in the NATO alliance and is key to the US-led fight against ISIS - deteriorated sharply in the last year of the Barack Obama administration.
"Rex Tillerson has said that he would like to come to Turkey on March 30," Mr Cavusoglu said in an interview with broadcaster Haberturk.
"I have told him that we will be in Ankara and available and would happily host him," Mr Cavusoglu said.
Mr Tillerson was likely to also meet with Turkish President Tayyip Erdogan and Prime Minister Binali Yildirim, he said.
Mr Erdogan and the Turkish government want the United States to extradite Fethullah Gulen, a US-based Islamic cleric who Ankara blames for orchestrating last year's failed coup. Gulen denies involvement in the coup attempt.
Ankara has also been angered by US support for the Kurdish YPG militia fighting ISIS in Syria. It is adamant that Washington should switch support for the planned Raqqa offensive from the YPG militia to Syrian rebels that Turkey has trained.
For the US administration, nervous about whether the Turkish-backed force is large enough and sufficiently trained, the decision sets Mr Trump's wish for quick battlefield victories against the need to maintain its strategic alliance with Turkey.
Ankara views the YPG as the Syrian extension of the Kurdish PKK militant group, which has fought an insurgency in Turkey's southeast since 1984 and is considered a terrorist group by both the United States and European Union.
Mr Erdogan believes ties will improve under Mr Trump. A phone call between the two earlier last month was positive, sources in Mr Erdogan's office have said.