Gilani met Interior Minister Rehman Malik, who briefed him about the status of the inquiry into the attacks that killed nearly 180 people in November last year.
Earlier in the day, Foreign Minister Shah Mahmood Qureshi met Gilani and discussed the premier's bilateral engagements on the sidelines of the Non-Aligned Movement summit in the Egyptian resort of Sharm-el Shaikh, including his meeting with Singh on July 16.
Qureshi also briefed Gilani about his meetings during his recent visit to Italy.
Indian External Affairs Minister S M Krishna was among those Qureshi met in that country. A statement issued by the Prime Minister's office said Gilani will hold talks with Singh "in a bid to restart the stalled peace process" between India and Pakistan.
India put the composite dialogue process with Pakistan on hold in the wake of the Mumbai attacks. It has linked the resumption of talks to Pakistan taking action against perpetrators of the attacks.
"We hope they would take some steps in that direction (punishing the perpetrators) and with this hope I will meet Gilani," Singh told mediapersons while returning home from the Italy after attending the G-8 summit.
Ahead of the Gilani-Singh meeting, Pakistan Foreign Secretary Salman Bashir will meet his Indian counterpart Shivshankar Menon on Tuesday to review the progress made by Islamabad to bring to book perpetrators of Mumbai attacks.
Interior Minister Malik told mediapersons on Saturday that the trial of five accused arrested by Pakistani authorities for alleged involvement in the attacks will get underway this week.
He also said investigators had identified 13 new suspects. Five Lashker-e-Taiba operatives -- including operations commander Zakiur Rehman Lakhvi and computer and communications expert Zarar Shah -- are currently being tried by an anti-terror court for their alleged role in planning and facilitating the Mumbai attacks.
The prosecution is expected to file a second chargesheet against the accused at the next hearing of their case on July 18.