The Daily Star says United were willing to smash their transfer record to lure the Uruguay hitman to Old Trafford from Paris Saint Germain in an £80m deal.
It is understood United bosses sounded out Cavani several months ago about a possible move and were willing to offer him a contract worth around £280,000-a-week.
But Cavani has changed his mind and snubbed United because he reckons they are a club in decline.
A source close to Cavani told the Daily Star: "He is well aware of United's interest in him and at one stage this might have seemed like an attractive proposal.
"But the fact is Manchester United can no longer offer him the standard of football he wants or thinks he deserves.
"The club is going through huge changes and he doesn't feel the time is right to even consider going to Old Trafford."