The Kathmandu Post, quoting people familiar with the talks on Wednesday, said Jaishankar paid a courtesy call on Oli to convey Prime Minister Narendra Modi's message of "seeking a new perspective on bilateral ties since both countries had gained political stability".
During the hour-long meeting, Jaishankar told Oli that a positive environment has been created in both countries to take policy decisions, said officials.
In his message to Oli, Modi expressed his readiness to make bilateral ties dynamic and progressive, Rajan Bhattarai, Oli's foreign relations advisor, told the Post.
Nepal-India ties hit a low after promulgation of Nepal's Constitution in September 2015. New Delhi had imposed an over five-month-long border blockade, which created hardships in Nepal.
Oli on Wednesday conveyed to Jaishankar that he has "special relations with Modi" and they have spoken about the development and prosperity of both nations, according to Bhattarai. Jaishankar, on his part, said India was ready to support Nepal in every endeavour.
"The central message at the political level was that we are entering into a new chapter in bilateral ties," said Bhattarai.
Oli and Jaishankar also discussed briefly the situation in Jammu and Kashmir after India's repeal of the state's special status.
A top security official told the Post that Jaishankar asked for a clearer position on Jammu and Kashmir, rather than what Foreign Minister Pradeep Gyawali told the media during a press conference on Monday.
Although the government has refrained from issuing an official statement on Kashmir, Gyawali, responding to a question during Monday's press conference at the Foreign Ministry, said, "The Nepal government is in favour of regional peace and stability. The dispute should be resolved through talks and we firmly believe that the government of India has the acumen to resolve the dispute peacefully."
Jaishnakar went on to inquire after Oli's health as he will be going to Singapore for medical treatment.
( With inputs from IANS )