Nkunku is currently out of favour at Stamford Bridge, with Enzo Maresca preferring Nicolas Jackson up front.
United's forwards have underperformed this season, prompting the club to explore new options.
The potential loan deal is particularly interesting as Chelsea have shown interest in United winger Alejandro Garnacho.
The Athletic states that there is likely to be some link between the two deals if they happen.
United want Nkunku on loan, while Chelsea would much rather a permanent sale.
