The visit comes nearly three months after the two countries decided to establish a joint ministerial commission to formulate a framework to strengthen ties in sectors like energy, trade, investment, manpower and labour and information technology.
Kuwaiti Foreign Minister Sheikh Ahmed Nasser Al-Mohammad Al-Sabah visited India in March during which both sides decided to set up of the joint commission.
Jaishankar is likely to carry a letter from Prime Minister Narendra Modi for Kuwaiti Emir Sheikh Nawaf al-Ahmad al-Sabah on ways to enhance bilateral ties, the sources said.
During his visit to India, Al-Sabah said that the "catalogue of cooperation" between India and Kuwait is vast and that there were lots of avenues to explore further.
It was announced during Al-Sabah's visit to India that the joint commission at the level of foreign ministers will steer the relationship and will act as an umbrella body for all bilateral institutional engagements.
Kuwait has been supporting India in dealing with the coronavirus pandemic by supplying relief material as well as medical oxygen.
Indian Navy ships have brought large quantity of medical oxygen from Kuwait in the last few weeks.