The former Mis-Teeq singer replaced Arlene Phillips on the judging panel of the reality talent contest earlier this year.
Dixon told The Mirror: "The series has gone so quickly, I'll be quite sad when it finishes.
"Obviously music is my first job. I'm making my second album and probably going to America but I'd love to do Strictly again.
"This year has been very positive. I worked for years to get my own solo tour and a successful solo album. Getting into the TV side of things as well, I think, 'Wow'."
Of her controversial appointment, she added: "I had the complete media onslaught. By the second weekend I felt like I was on trial. That was tough. But it brings out the fighting spirit in you.
"If things aren't going well you have to rise above it in the most positive way you can and show your true character. Fortunately, things are great now."
A BBC spokesman said: "Alesha has been doing a first class job and we look forward to having her back next year."