Morata is on loan at Juve from Atletico Madrid but reports in Spain suggested the former Real Madrid striker was poised to join Los Blancos' Clasico rival Barcelona.
AS reported that a deal was "95 per cent" done for the Spain striker to join on a six-month loan deal with a purchase option included, with Barca coach Xavi reportedly keen to make him the latest addition to his forward ranks after the arrival of Ferran Torres from Manchester City.
However, speaking prior to Friday's (AEDT) Serie A clash with Napoli, Allegri said he has no intention of letting Morata end his second stay in Turin.
"Alvaro Morata will not leave, he is a [high] performance footballer. The problem with him is that he is given a wrong label," Allegri said.
"He is very important: I talked to him and I told him not to leave. Case closed."
However, Wales midfielder Ramsey, who earns a reported £400,000 ($750,000) a week at Juve, looks increasingly likely to move back to the Premier League.
The 31-year-old has been linked with a return to Arsenal, as well as Newcastle United, which has money to spend after its big-money takeover. Everton has also been credited with an interest, while a formal approach by Burney was reportedly rejected by Ramsey.
Allegri added: "Aaron Ramsey is now set to leave Juventus. We're working on it.
"There are no other changes or transfers in our plans, this is 99 per cent sure."
Juventus is fifth in Serie A and 12 points adrift of leader Inter Milan ahead of the resumption of the league after the mid-season break.