The meeting comes just days after Singh resigned as the Chief Minister of Punjab and amid the ongoing crisis in the Punjab unit of the Congress party.
However, Singh's media advisor Raveen Thukral denied his meeting with Shah and Bharatiya Janata Party (BJP) chief J.P. Nadda, saying he's on a personal visit to Delhi to meet some friends.
"Too much being read into @capt_amarinder's visit to Delhi. He's on a personal visit, during which he'll meet some friends and also vacate Kapurthala house for the new CM. No need for any unnecessary speculation," Thukral tweeted.
Singh also said that he is on personal visit. There is also speculation that former Punjab Chief Minister, who was recently asked to resign, may join the BJP.
Sources however said that the two leaders discussed about the ongoing farmers' protest in Punjab and the political situation in the State.
