According to ESPN, the two London clubs turned down the chance to sign the 26-year-old, who spent the second half of last season on loan at Juventus.
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Chelsea have already managed to sign Liam Delap and Joao Pedro, while Viktor Gyokeres is reportedly moments away from finally becoming an Arsenal player.
United have previously been linked with all three of those players but have as of yet failed to sign a new out-and-out striker.
The report adds that Ruben Amorim’s side are keeping tabs on the Paris Saint-Germain forward’s situation, but they also like Aston Villa's Ollie Watkins and Juventus' Dusan Vlahovic.