Singh has been keen on having good ties with Pakistan, though he said the right time for a trip hasn't come as such a high-level visit would require a "suitable outcome".
"There are enough indications - the positive things he said during the high-voltage election campaign about the ties and his keenness to go back to pick the threads of unfinished peace process in 1998 - to show that Sharif is keen on having good ties with India," said a government official.
But his soft spot for fundamentalist outfits, some of them anti-India, is an open secret and how far will he be able to influence the military's stance on India is something to watch out for.
In addition, the progress on core issues such as Kashmir, Siachen and Sir Creek remains a matter of high-level political call on both sides.
Rajiv Gandhi was the last Congress Prime Minister to visit Pakistan in 1989.
Meanwhile, the BJP blamed the PM for hurriedly inviting Sharif.
"The Prime Minister should have waited and seen if Pakistan's attitude towards India improved before inviting him here," said BJP vice president Balbir Punj.
But CPM general secretary Prakash Karat supported the move and said Singh should also visit Pakistan.