BRUSSELS—The European Union’s executive is set to give its backing to Ukraine’s bid for visa-free access to the bloc, EU officials said, a step likely to stir disquiet among some member states already struggling with this year’s migration crisis.

Ukrainian President Petro Poroshenko has made visa-free access to the EU a key goal of his administration. It would symbolize the westward shift since the ousting of former President Viktor Yanukovych, and be a welcome sign of support from Europe as the country struggles with pro-Moscow...