Madrid and Juve are two of the four teams to have booked a place in the last eight of the competition, with the draw for the quarter-finals set to take place on Friday.
Zinedine Zidane's side are seeking a third consecutive Champions League title after Madrid saw off Paris Saint-Germain in the last 16.
Juve meanwhile came from behind in dramatic circumstances to beat Tottenham 4-3 on aggregate.
And while Allegri feels Madrid are the team to beat, he also wants to avoid Barcelona in the last-eight draw should they make it through.
"I think Madrid are the favourites to win the competition. They're focusing solely on the Champions League and there's nobody else that deals with games in this competition like they do."
Barcelona host Chelsea on Wednesday in the second leg of their last-16 clash having been held to a 1-1 draw at Stamford Bridge.