The idea was "heartily welcomed" by the locals.
Addressing the joint session of Bhutanese parliament, Modi said Indian states in the northeast had similar tastes and habits like the two Himalayan countries.
"Why can't we hold a special hills festival? We can hold an annual sports meet. Through sports we can connect the people. Sports brings sportsman spirit, which contributes to happiness," he said, and asked the Indian states, as also Bhutan, to think over the proposal.
Reacting to the suggestion, Tenzing Lamsang, the editor-in-chief of the largest circulated English weekly "The Bhutanese", said "It's a very good idea. It will encourage people-to-people contact.
"Nothing can build relations better than sports. At the same time it will help in developing Bhutan's sports infrastructure.
Bhutan, whose population of around 750,000 is smaller than most Indian states, has a football team and is nurturing a national cricket side.
However, in the absence of a proper sports infrastructure Bhutan has not been able to host the South Asian Games.
While describing the suggestion as "wonderful", Bhutan Football Federation president Ugyen Tsechup said it could give a fillip to developing the sports framework in Bhutan.
"Because once we have the set up in place, we can invite sports persons from the northeastern states and himalyan region nations."