Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph structure. In particular, we show that an almost maximal-entropy random walk is obtained when the step probabilities are proportional to a power of the degree of the target node, with an exponent $α$ that depends on the degree-degree correlations, and is equal to 1 in uncorrelated graphs. ; Comment: 4 pages, 1 figure, 1 table + 1 page supplementary material