A central problem in low-dimensional topology is to get some topological understanding of quantum invariants. The universal sl2 invariant of string links has a universality property for the colored Jones polynomial of links, and takes values in the h-adic completed tensor powers of the quantized enveloping algebra of sl2. Milnor’s invariant is a classical invariant which is a generalization of the linking number. Habegger and Masbaum showed that Milnor invariants are obtained from a reduced version of the Kontsevich integral. The universal sl2 invariant is a series of finite type invariants, and thus is theoretically obtained from the Kontsevich integral by using a weight system. In this talk, we give a partial construction for such a weight system, and study relationships between Milnor invariants and the universal sl2 invariant. This is a joint work with J.B. Meilhan.