Singh, who is known as the architect of economic reforms, was also the Finance Minister of the country from 1991 to 1996 in the then Narasimha Rao government.
There was no official statement on the meeting which is seen as a courtesy call.
What transpired at the meeting is not known, but coming ahead of the first Union Budget of the new government to be presented by Sitharaman on July 5, it understood to have centred around the economy.
Sources said, though a courtesy meeting, the Finance Minister may have discussed what needs to be done to bring the economy back on the growth path.
Singh was also the Governor of the Reserve Bank of India from 1982 to 1985, and the Deputy Chairman of the Planning Commission of India - now called Niti Aayog - from 1985 to 1987.
On July 5, the BJP-led NDA government will unveil the Union Budget for the financial year ending March 2020. On February 1, Piyush Goyal had presented the interim Budget.
It is for the first time in nearly 30 years that Singh will not be in Parliament during the Budget Session after his tenure of nearly three decades as a Rajya Sabha member ended earlier this month.
The Indian economy is going through a tough period with growth at a five-year low at 6.8 per cent, and low consumption.
( With inputs from IANS )