The post has been lying vacant for a year in the wake of resignation of Krupa Shanker Singh following party's defeat in the civic elections in Mumbai in February last year.
An indication of an early decision on the new Mumbai unit chief came at the meeting of the Congress MPs from Maharashtra including those from the megapolis.
Incidently, before the meeting Gandhi had a 30-minute meeting with former Union Minister Gurudas Kamat, MP, who is a former Mumbai Congress chief.
Bajwa's appointment as the Punjab Congress president marks the apparent beginning of the much-delayed organisational shake-up across states where the party hopes to put its house in order.
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The party has makeshift arrangements in many states where party chiefs had submitted their resignations to Congress president Sonia Gandhi several months ago but are still continuing on the posts as the leadership is yet to find replacements.
Bihar Congress president Mehboob Ali Kaiser had resigned soon after the party's debacle in 2010 assembly elections but he continues to hold the charge.