The party said she would have to seek re-selection as its candidate after reconsidering her decision to step down.
The 77-year-old MP announced in February she would retire after more than 30 years in Parliament but said in September she had changed her mind.
It followed a row over a party decision to impose an all-women shortlist.
The three other contenders have been named as Cardiff-based PCS union official Katie Antippas, Rhondda Cynon Taf councillor Sue Pickering, and scientist Aysha Raza, a Labour councillor in Ealing, west London, originally from Aberdare.
Ms Clwyd said in September that local voters had asked her to reconsider her retirement, and said she had received a "very enthusiastic" reaction to her change of heart.
It followed a row over Labour's decision to use an all-women shortlist to select her successor, which has been strongly opposed by the local party.
Ms Clwyd, a former Labour shadow minister, has been outspoken on the state of the NHS following failings in the care of her husband at the University Hospital of Wales, Cardiff, in the days leading up to his death.
David Cameron appointed her as an adviser on how hospitals in England should handle complaints.
Ms Clwyd has represented the Cynon Valley since winning a by-election there in 1984.
Under Labour party rules a serving MP can be re-selected by a "trigger ballot" if more than 50% of local party members agree to back them.
However, sources within the Labour party questioned whether there was sufficient time to organise a trigger ballot in Cynon Valley before the 2015 general election in May.
A Welsh Labour spokesperson said earlier in November: "Under established procedures a full selection takes place where a sitting MP announces their intention to stand down."
The candidate will be chosen by local party members in December.
MP Ann Clwyd faces a challenge from three other women to defend Cynon Valley for Labour at the 2015 election.