Under Guinea's constitution, presidents may only serve two terms.
Conde, 82, was elected president in 2010 and again in 2015. But this year he pushed through a revamped constitution that opponents say was crafted to reset the term counter, enabling him to run again.
His Rally of the Guinean People (RPG) party announced that it wanted Conde to run again at a convention in the capital Conakry.
Party members are issuing a "plea to President Alpha Conde to accept the will of the people to be the RPG's sole candidate," MP Diakagbe Kaba told delegates.
The president has yet to formally respond to the request. He has previously said that "the party will decide" who goes forward to the poll.
Guinea's electoral commission has proposed the presidential election be held on October 18, but Conde has yet to sign off on a date.
Thursday's announcement is likely to incense Guinea's embattled opposition, which has staged mass rallies since October against the possibility of Conde running for a third term.
Security forces in the former French colony repeatedly cracked down on the protests, in which several dozen civilians were killed.
Opposition figures also attempted to organise a boycott of the referendum in March, but the vote went ahead despite protests.
According to the official results, the constitution was approved by 91.59 percent of those voting, with a turnout of 61 percent
Conde is a former opposition figure himself who was jailed under Guinea's previous iron-fisted regimes.
Hopes of a new political dawn flowered when Conde became Guinea's first democratically elected president in 2010, but critics say he has become increasingly authoritarian.