Congress President Sonia Gandhi and Prime Minister Manmohan Singh have held three meetings so far on the reshuffle but no official word is out on the issue.
Speculation was rife that it could be on Monday but chances appear to be brighter on Tuesday.
However, sources said Trinamool Congress Chief Whip in the Lok Sabha Sudip Bandhyopadhyay may finally get a break and could be inducted as Minister of State, possibly in the Finance Ministry in charge of Revenue.
There is also speculation that incumbent Minister of State Finance in charge of Revenue S S Palanimanickam may be upgraded to Cabinet rank in the wake of resignations by his DMK colleagues A Raja and Dayanidhi Maran from the Cabinet.
The talk in Trinamool Congress is that Mamata Banerjee could entrust senior leader Dinesh Trivedi with the Railways portfolio she vacated after becoming the West Bengal Chief Minister.
DMK may opt for the upgrade in view of the fact that it is said to be not in a mood to name new entrants into the government at this juncture when two of its ministers had to resign under a cloud and party chief Karunanidhi''s daughter Kanimozhi is in jail.