The 19-year-old signed a £166million permanent deal with Paris Saint-Germain from Monaco this summer, but PSG are being investigated over financial fair play and face big fines if found guilty.
United have registered their interest with the teenager's advisers, the paper says, and would be willing to sacrifice winger Anthony Martialin part exchange.
City, meanwhile, have have already made it known that manager Pep Guardiola would like to add the striker to his squad, the paper adds.
