The attacker was being linked with loan or permanent moves away from the club.
The Brazilian arrived at Old Trafford for £86 million in the summer that Erik ten Hag took over as manager, having played for the Dutchman at Ajax.
Brazilian side Sao Paulo were hoping to secure his signature, but do not appear to have a chance.
“Talking to President Julio Casares, he assured that there is no possibility of this deal happening, it is something completely out of the reality of São Paulo. Antony is not coming back now, his priority is Manchester United,” the winger's agent Junior Pedroso told Jorge Nicola, via Portal Do Sao Paulino.
On Antony’s signing, Ten Hag told AD Sportwereld: “I don’t go over the budget. I’ve never even had a budget. At United, the budgets lie with the owners and management. He certainly showed that potential in the first month: he scored three times in his first three games.
"After that it became more difficult, last season was not good. But I am still convinced that he has the potential to play at this club. We want this club back to where it was more than a decade ago, to a club that wins the Premier League, which can win Champions Leagues.
"We are really a long way away from that, I think. I think we’ve taken steps since then, otherwise we wouldn’t have won two prizes. But we are not yet so far that a ‘winning culture’ already prevails here in all respects. Our standards, our norms and values, still need to go up."