The report has claimed that Modi is not too keen about his US trip. However, Modi may visit US in September this year to address the United Nation General Assembly in New York.
In July, he is expected to visit Brazil to participate in BRICS summit.
Modi has received congratulatory messages from several world leaders, since BJP's grand victory on May 16.
Modi with US
"US congratulates BJP on its victory in India's historic election", US President Barack Obama's National Security Council had said on Friday.
On Tuesday, Modi had a telephonic conversation with the US President Barack Obama where they talked about further strengthening India-USA strategic partnership that will help both nations.
After shunning him for over a decade, US is warming up to Narendra Modi with a fresh invitation to visit Washington and recalling its envoy headed home four days before he becomes India's new prime minister.
Modi has had an uneasy relationship with the US which denied him a visa over 2002 Gujarat riots.
Modi, during his US visit would be eligible for an A-1 visa, State Department Spokesperson Jen Psaki has said.
"The Prime Minister of India will be welcomed to the United States. As Head of Government, Modi would be eligible for an A-1 visa," she said.
Saying he could become India's 'Nixon', a Chinese strategic thinker on Tuesday said India's prime minister-designate, Narendra Modi, can help resolve their dragging border dispute.
Modi with China
Even before the Lok Sabha results were to be announced, an influential state-run Chinese daily, Global Times had said, "If BJP prime ministerial candidate Narendra Modi comes to power, it could bring India and China closer."
On Tuesday, Modi thanked all the leaders on Twitter who congratulated him on his victory.
Modi with Japan
To Japanese Prime Minister Shinzo Abe, Modi thanked him for extending his good wishes, while saying "strong relations with Japan is beneficial for both our nations."
"Personally, I have a wonderful experience of working with Japan as CM. I am sure we will take India-Japan ties to newer heights."he wrote on Twitter.
Modi with Russia
On Monday, Putin had said to Modi in a congratulatory message, "We highly appreciate traditionally friendly relations between the two countries based on the declaration of strategic partnership."
To Russian President Vladimir Putin, Modi tweeted: "I thank President Putin for his good wishes. Looking forward to making our relations with Russia even stronger in the years to come. India-Russia friendship has stood the test of time."
"We will further strengthen our relations in a wide range of fields," he wrote in two tweets.
Modi has invited heads of all the South Asian Association for Regional Cooperation (SAARC) members for his swearing-in ceremony, that will take place on May 26 at 6 pm.