Erdogan, himself a former footballer, met Platini at the ruling AK Party's headquarters in Ankara on Monday ahead of the UEFA Executive Committee meeting in Istanbul on Tuesday and Wednesday.
The UEFA Congress of Europe's 53 national associations will be held in Istanbul on Thursday. Host venues, including stadiums for the 2014 UEFA Champions League and Europa League finals, will be appointed at the Executive Committee meeting.
Erdogan and Platini discussed the match-fixing probe, under which 93 people including the chairman of champions Fenerbahce are being tried in an Istanbul court, Radikal newspaper reported.
The allegations emerged last July when police detained those accused of involvement in rigging 13 matches, including Fenerbahce's 4-3 victory over Sivasspor which clinched the league championship on the final day of last season.
Alongside Fenerbahce and Sivasspor, the indictment also names Besiktas and Trabzonspor. Fourteen players are among the defendants.
Radikal newspaper said Platini had told Erdogan in their talks that it would be a good idea for Fenerbahce to withdraw a 45-million-euro case which the club has opened against UEFA at the Court of Arbitration for Sport (CAS) over its exclusion from this season's Champions League.
No statement has been issued on the content of the talks, which officials described as a courtesy visit, and the Radikal report could not be confirmed.
Monday's talks were also attended by Turkey's sports minister, UEFA's Turkish vice president Senes Erzik and the new chairman of the Turkish Football Federation (TFF), Yildirim Demiroren.
Former Besiktas chairman Demiroren was elected as TFF chairman last month with the task of quickly resolving the match-fixing crisis. Sanctions against clubs involved could include relegation or the deduction of points.
Fenerbahce Chairman Aziz Yildirim, who is accused of being a gang leader, has denied the match-fixing charges, saying the allegations against him were specifically designed to undermine the 18-times domestic champions.
UEFA general secretary Gianni Infantino was scheduled to hold a news conference on Wednesday after the Executive Committee meeting.
