With Dr Singh set to be sworn in on Friday for a second term, Congress negotiators, led by senior leader Pranab Mukherjee, are grappling with the issue.
A meeting slated for 10.30 am on Thursday between Dr Singh and the President on government formation was deferred apparently because the list of the Council of Ministers was yet to be finalised.
Indications are that Mukherjee is likely to get the finance portfolio while P Chidambaram and A K Antony are expected to retain home and defence respectively.
Among the probable names doing the rounds for some key ministries are Kapil Sibal for human resource development replacing Arjun Singh, who is likely to become a governor.
Salman Khurshid is likely to get the minority affairs ministry, held by A R Antulay, who was defeated in the election.
A tussle is reportedly on wresting the railway ministry, held by Rashtriya Janata Dal chief Lalu Prasad who is unlikely to find a berth in Manmohan Singh's second Cabinet.
Trinamool Congress chief Mamata Banerjee is eyeing the railways portfolio as also the DMK.
Kamal Nath is being mentioned for the external affairs portfolio.
Reports had it that the DMK is seeking as many as nine ministerial berths while the Trinamool Congress is insisting on getting one minister more than what the DMK is given.The Trinamool has 19 MPs; the DMK 18.
The DMK is said to be keen on five Cabinet berths and four ministers of state slots. It is said to be eyeing the health, telecom, power, surface transport and railways ministries.
It wants ministries to be given for debutant MPs M K Azhagiri and Kanimozhi, Tamil Nadu Chief Minister and DMK chief M Karunanidhi's children, his grand-nephew Dayanidhi Maran and A Raja and also for new entrants T K Elangovan, Helen Davidson and Jagatrakshakan, a third-term MP.
Besides Mamata Banerjee, probables Trinamool Congress ministers include Dinesh Trivedi, Sudip Bandhopadhyay, Sultan Ahmed and Mukul Roy.
Sushilkumar Shinde and V Kishore Chandra Deo may be in the running for the Lok Sabha Speaker's post.
Some new entrants in the Lok Sabha like Mallikarjun Kharge (Karnataka) and Manicka Tagore (Tamil Nadu) are also doing the rounds for induction in the ministry.
Other probables include young MPs Sachin Pilot, Naveen Jindal, Jyotiraditya Scindia and Jiten Prasada.