The Leicester City striker is available for transfer this month.
However, Claude Puel is reluctant to loan Slimani, signed from Sporting Lisbon for £28million in the summer of 2016, to a Premier League club.
The 29-year-old would cost around £20million, though Leicester may be prepared to loan him with an obligation to buy.
United's move for Slimani comes after Liverpool's Daniel Sturridge chose to join West Bromwich Albion on loan. The club also failed to meet Feyenoord's £20million valuation for Nicolai Jorgensen.