Kim has reportedly expressed a willingness to engage in "bilateral and multilateral talks", but it is unclear if that indicates a willingness to rejoin the six-nation discussions.
Wen's "goodwill" visit coincides with the 60th anniversary of formal ties between the two communist neighbours and is likely to be dominated by ceremony, but it is hoped that the presence of such a senior figure can ease tensions over Pyongyang's nuclear activities.
"This visit will be mostly focused on bolstering bilateral relations and the 60th anniversary, but the nuclear issue is sure to come up," Zhu Feng, a professor of international security at Peking University, said.
"The key question will be whether North Korea goes beyond its recent statements and directly expresses willingness to return to the six-party talks."
Wen is heading a delegation that includes Yang Jiechi, China's foreign minister; Wu Dawei, the vice-foreign minister and a senior envoy on North Korean issues; Liu Zhenqi, a general; and other high-ranking officials.
Chinese officials have released few details about the itinerary of the visit.
"If there is any country that can convince the North Koreans to go back to the negotiating table it would be China," Al Jazeera's Melissa Chan, reporting from Beijing, said.
"Although, over the past two years the relationship between the countries has been strained. The Chinese do not feel they have been consulted on a lot of major decisions the North Koreans have been making."
Talks on Pyonyang's nuclear programme have unfolded in fits and starts, with North Korea taking some steps to disable its nuclear facilities after agreeing an aid-for-disarmament deal in September 2005.
However, it has carried two nuclear tests since, first in 2006 and then in May this year.
Despite condemnation from the UN Security Council over its nuclear testing, the North followed the test in May with several further missile tests, ratcheting up tension with Japan and South Korea.
But in recent weeks, the North has made overtures to China, the US and South Korea, most recently allowing meetings of family members separated by the 1950-53 Korean War.