Juventus chief executive Giuseppe Marotta was adamant on Monday that the Chile star would only be sold if he expressed a desire to leave Turin, while Vidal insisted he is "not going to Manchester" last week.
Goal understands Vidal met with his agent and senior officials on Sunday evening to discuss the possibility of a transfer to Old Trafford but Allegri has ruled out a move following a training session on Tuesday.
"Vidal will stay here and he's very happy about this," he told reporters. "I spoke with him about his fitness, we're happy he will stay with us."
United had hoped to tempt the goalscoring midfielder into a move to the Premier League by offering a wage package of £250,000 per week, with Louis van Gaal making him one of his key transfer targets.
Vidal returned to training with Juventus on Monday after representing his country at the World Cup and confirmed last week he was to speak to his new manager regarding his future when the pair met.
"I don't know if I will stay at Juventus, I'm happy here in Turin," he said on Thursday. "I will talk with Allegri on Monday. I'm not going to Manchester."