The star praised Franklin's vocal talents, but said that she is also impressed with a number of other female artists.
Asked who she believes is the greatest singer of all time, she told radio station Magic: "Aretha Franklin - but there are many, and all different.
"Whatever you feel about Mariah Carey, when you hear her sing, oh my God! I've never heard a voice like that! Whitney Houston is another incredible singer, Shakira, Beyoncé, all these girls."
Lennox, who released her festive LP A Christmas Cornucopia last month, also admitted that she has always had a passion for singing carols.
She explained: "When I record something it's there forever and that's such a lovely feeling.
"Carols have such potential for power and passion. Singing is an energetic thing and I enter fully into that song."
It was recently reported that Lennox had axed plans to promote the LP on a festive TV special.