According to sources, a decision in this regard is expected to be taken after Prime Minister Narendra Modi returns from hi Nepal trip.
Singh held discussions with Shah and senior party leaders JP Nadda and Ram Madhav at Gujarat Bhavan in a bid to resolve the ongoing controversy.
Later in the evening, he also met Home Minister Rajnath Singh at the latter's residence, sources said.
According to the sources, the government is studying Verma Committee report that examined the possibilities of changing the pattern of civil services examination among other matters, and is working out an amicable solution for the problem, which has rocked Parliament for the past week.
Singh had also met Rajnath earlier on Saturday over the issue.
Various opposition parties have demanded an early resolution to the matter as the civil services aspirants continued with their protest.
The students have been protesting in the national capital in support of their demand to change the pattern of Civil Services Aptitude Test (CSAT) to give level-playing field to those coming from rural areas.
They have objected to the level of aptitude, analytical and English language questions being asked in the CSAT II examination, claiming they are biased in favour of those aspirants with engineering and management background.
The protesting students have also been demanding that the civil services preliminary examination, scheduled to be held on August 24, be postponed.

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