Emeritus Senior Minister Goh Chok Tong has sketched out what he hopes would be a timeline for the formal designation of the next prime minister - the first time a senior figure from the People's Action Party has done so.
According to this timeline, Singaporeans could know who their next leader is before the year is over.
Writing in a Facebook post on the last day of 2017, Mr Goh said that the issue of the fourth-generation (4G) leadership is "one urgent challenge I would like to see settled".
He added: "Every succession is different, but one thing remains the same: Each cohort will have to pick one amongst themselves to lead, and support him.
"I hope the current cohort will do so in six to nine months' time. Then PM (Lee Hsien Loong) can formally designate their choice as his potential successor before 2018 ends."
PM Lee has said that he hopes to hand over the reins of government to the next leader by the time he is 70, in 2022.
Observers say having Mr Goh weigh in shows the issue is of utmost urgency.
Political observer Mustafa Izzuddin, noting that Mr Goh "is speaking from wisdom and experience", said this could well mean the identity of the next prime minister would be made known this year, "sooner rather than later".
There have only been two prime minister successions since Singapore's Independence, and Mr Goh was involved in both.
In 1990, he took over as prime minister from founding prime minister Lee Kuan Yew. In 2004, he handed over the role to the current Prime Minister - PM Lee.
Singapore Management University law don Eugene Tan agreed that the timeline should not drag on beyond this year, as the designated successor has to earn the trust and respect of Singaporeans and other stakeholders and "you can't hothouse and rush this process".
"Furthermore, the uncertainty can also undermine the 4G leadership's internal cohesion as the tacit quest to be first among equals will raise the stakes of competition if the process becomes long-drawn," he added.
Meanwhile, ISEAS - Yusof Ishak Institute fellow Norshahril Saat said that PM Lee's successor would need time to "settle into" the post of deputy prime minister.
He added that before taking on the top job, PM Lee himself was deputy prime minister for 14 years, while Mr Goh spent five years as first deputy prime minister.
This means that the next prime minister will have the shortest run-up phase.
Observers have said that there are just three Cabinet ministers left in the race to be the next prime minister - Minister for Finance Heng Swee Keat, labour chief and Minister in the Prime Minister's Office Chan Chun Sing and Minister for Education (Higher Education and Skills) Ong Ye Kung.
The appointment of one of these three as deputy prime minister or first deputy prime minister could happen during the major Cabinet reshuffle that PM Lee has said will take place this year.
Associate Professor Tan said that an announcement late in the year would "allow for a final appraisal of the front runners by their peers".
Mr Goh had written in his post about the task that the 4G leadership faces, noting that "whoever is chosen, the team will have to work together, bring in others, and gel to form a cohesive fourth-generation Cabinet".
"They must write a new inspiring chapter for Singapore, be courageous to make difficult decisions, stand tall with integrity, and earn the respect and trust of Singaporeans and the world at large," he added.
"This is my wish for the new year - a Singapore in good hands, a Singapore that all of us build together."