Speaking in Istanbul Saturday, Gul said he would have considered running as a presidential candidate had there been "widespread agreement and desire" for him to do so.
The ex-president left politics in 2014 but his name is often floated as a possible competitor to President Recep Tayyip Erdogan, AP reported.
Erdogan announced presidential and parliamentary elections would be moved forward by more than a year to June 24, catching opposition parties by surprise.
Gul, a founding member of Erdogan's ruling party, briefly served as Turkey's prime minister following elections that brought the party to power in 2002. He served as Erdogan's foreign minister and Turkey's eleventh president.