Singh and Gilan attended the opening of the summit in Thimphu, Bhutan's capital, and Indian media quoted government sources as saying the meeting between the two men has been scheduled for Thursday evening.
The sources said Singh would voice India's concern that Islamabad is not doing enough to crack down on Pakistan-based fighter groups.
Shah Mahmood Qureshi, the Pakistani foreign minister, told reporters in Thimphu on Tuesday that any talks should address the need to resume a full-fledged peace dialogue.
"It's time for India to make up its mind whether it wants to engage or not .... Engagement is the only way forward," he said.
"We need to go beyond a handshake," Qureshi said, referring to Singh and Gilani's cursory exchange of pleasantries at a summit on nuclear security in Washington earlier this month.
India suspended dialogue with Pakistan after the 2008 Mumbai attacks, which killed at least 166 people and were blamed by New Delhi on Pakistan-based fighter groups.
But contact was tentatively resumed at a meeting of senior foreign ministry officials in Delhi last February, although India insisted that proper dialogue would only resume if Pakistan brought to justice those responsible for the Mumbai killings.
Qureshi said it was time for India to move forward and stop demonising Pakistan.
"We have to accept terrorism is a common challenge. It's not us and you, it's a collective effort," he said.
Qureshi attended a meeting of Saarc foreign ministers on Tuesday along with SM Krishna, his Indian conterpart, who urged member states to "rally against the forces of terrorism".
"The South Asian region is particularly afflicted by this menace," Krishna said.
Saarc, formed in 1985, brings together Afghanistan, Bangladesh, Bhutan, India, the Maldives, Nepal, Pakistan and Sri Lanka.
Bhutan is hosting the summit for the first time and it wants to focus on climate change and launch a $300m development fund for infrastructure.
Ciritics say Saarc has achieved very little 25 years since its formation largely due to the volatile relationship between India and Pakistan.