Pakistan is hosting a 14-nation ministerial-level conference on December 8 to discuss regional cooperation on Afghanistan. Swaraj has been invited but New Delhi has so far given no indication whether she will attend.
However, informed sources said here that prospects of the Indian minister's visit were "fairly bright" but a final decision was likely to be announced by Friday.
After the cabinet meeting, Swaraj had stayed back and held discussions with Prime Minister Narendra Modi for nearly 20 minutes.
"It is not final so far," she said replying to a specific question that whether she was travelling to Pakistan next week.
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Swaraj's possible visit may also indicate breaking of impasse created in Indo-Pak ties after the cancellation of a meeting between the NSAs of the two countries in August amid mutual blame game.
Significantly, Prime Minister Narendra Modi held a brief but warm chat with his Pakistani counterpart Nawaz Sharif on the sidelines of climate meet in Paris last Monday after which Sharif told Pakistani media that the talks were held in a "good way, in a good environment".
The US also welcomed the brief meeting between Modi and Sharif in Paris.
"We always welcome these kinds of exchanges and dialogue between India and Pakistan," State Department Deputy Spokesperson Mark Toner told reporters yesterday when asked about the meeting.
Last month, Pakistan had lodged an FIR in the Pathankot
terror attack case which was seen by India as a "step forward" in bringing the perpetrators of the strike to justice.
India had submitted evidence to show that the six perpetrators who attacked the air base came from across the border, and demanded action against the terror group Jaish-e-Mohammed led by Azhar.
Yesterday, Pakistan Prime Minister Nawaz Sharif's Foreign Affairs Advisor Sartaj Aziz said the SIT may visit India in the next few days and hoped that the Foreign Secretary-level talks will be scheduled very soon.
Pakistan had last week set up a five-member Joint Investigation Team (JIT) to probe the terror attack.