Party sources said that the Law Minister was in contact with Kejriwal even as the government was reportedly exploring various options on breaking the logjam.
The sources said that Congress President Sonia Gandhi, who is recuperating after having undergone a surgery, has been kept in the loop about the developments back home and she could come back by the month end.
Union Minister Vilasrao Deshmukh, a former chief minister of Maharashtra from where Hazare hails, was being speculated in the media as one who could be the government's emissary but sources close to him said he has not not been sounded on the subject.
Deshmukh met Finance Minister Pranab Mukherjee in a meeting in the morning in which Agriculture Minister Sharad Pawar, also from Maharashtra, was present.
Highly placed sources in the Congress said the possibility of appointing any minister officially to talk to Team Anna does not seem a likelihood at least for now.
The Congress leadership is hopeful that something will work out towards resolution of the controversy by the end of this week.
The party is pinning hopes for some forward movement after the all-party meeting convened by the Government on Wednesday.
"The main concern as of now is the health of Anna Hazare," a senior party functionary said speaking on the condition of anonymity.
Meanwhile a party MP speaking on the condition of anonymity said that there is a sense of worry and concern among the young MPs with the development as Hazare's agitation was snowballing into a problem in their constituencies.