Turkish media, including the NTV broadcaster, said the secular Republican People's Party (CHP) would join forces with the new Iyi (Good) Party as well as the conservative Saadet (Felicity) Party and the centre-right Democrat Party.
Turkey is due to vote in simultaneous presidential and parliamentary elections on June 24. The alliance would see the parties have joint lists for parliament although they would have their own separate candidates for president, the reports said. Talks between the parties were ongoing ahead of an expected signing of the alliance protocol on Thursday, a CHP source, who did not wish to be named, told AFP.
The alliance is in response to Erdogan's own partnership with the right-wing Nationalist Movement Party (MHP) earlier this year. The MHP is supporting Erdogan's bid for the presidency.
The four-way alliance will bring together a disparate collection of political forces united by a shared opposition to Erdogan.
The CHP sees itself as the watchdog of Turkey's secular traditions, the Iyi Party is a new nationalist formation, Saadet is religiously conservative while the Democrat Party was in power in the 1990s.
However the alliance notably does not include the pro-Kurdish Peoples' Democratic Party (HDP), currently the third biggest party in parliament but many of whose top figures are currently jailed.
Aksener earlier Wednesday submitted her formal application to run for the presidency to the Supreme Election Board (YSK).
The CHP and HDP are due to reveal their presidential candidates to challenge Erdogan on Friday. The HDP's ex-chief Selahattin Demirtas is in the frame despite being in jail since November 2016 while most analysts are at a loss to suggest a strong CHP contender.
The June 24 polls will be a landmark in modern Turkish history. After the elections, a new presidential system approved in an April 2017 referendum which critics claim gives the head of state authoritarian powers will come into force.
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