Ramsey is out of contract with Arsenal at the end of the season and is currently able to talk to rival clubs with a view to signing a pre-contract agreement. There is also a chance he could leave now for a fee in the region of £18 million and Juve along with the likes of Bayern Munich, have been linked with a swoop.
Juve are said to be in the box seat but speaking on the eve of the Italian Supercoppa against AC Milan in the Saudi Arabian city of Jeddah, Allegri cooled the rumours.
"I'm not talking about the transfer market," he said when quizzed about a possible deal for Ramsey. "He's an Arsenal player, and also the Juve squad is fine as it is."
That squad now includes Cristiano Ronaldo, who Allegri hopes will help him finally win the Supercoppa.
"Our aim is to win the league, as well as the Supercoppa, the Coppa Italia and the Champions League," he said. "We need to win as many trophies as we can and Ronaldo is important to us for this; he raises our level. If we win this, then people will say it's down to Ronaldo giving us more belief. Otherwise, that won't be the case. We'll see tomorrow. Of course he's used to games like these, having won four of the past five Champions Leagues, but let's not forget that Juventus have played two of the past four Champions League finals."