Krishna, who is here for the Shanghai Cooperation Organization (SCO) Summit, said he invited Li to visit India and the Chinese leader responded by saying that he had visited the country in 1985 as a youth Communist activist.
"India is not the same as it was in 1985, so I look forward to his (Li's) visit to India at his convenience," Krishna said.
Indian officials regard the meeting with Li significant as he is tipped to take over as premier from incumbent Wen Jiabao, who is set to retire along with President Hu Jintao and other top leaders after a decade-long stint in power.
Li is set to assume higher responsibilities, Krishna said.