Yeah don't see it.

Sayaka over idolizes Mami, and Mami seems to pay more attention to Madoka, because of her potential.

Mami does notice Sayaka, and wants to help her become a magical girl, but she spent more time with Madoka. She barely even considered Sayaka when Madoka offered to team up with her.

She exclaimed, "We can be a magical girl duo!" Not "We all can be a magical girl treo!"

Sayaka on the other hand, idolizes Mami with rose tinted glasses. She saw Mami as perfect, when Mami was anything but that. Mami lead the two into danger, and recklessly killed witches. If Homura didn't exist, Madoka and Sayaka would've been dead because Mami was so careless into leading the two girls into a witches labyrinth.

Sayaka also refused to trust any other magical girl, believing they were only after Grief Seeds, and yes, Mami did warm Sayaka about certain things, she didn't warn her about establishing a balance between protecting others, and protecting and caring for yourself.

The two won't be compatible. Not in the slightest.

Mami is a great character, but I assume after her and Kyoko went different ways she was so desperate to have friends that the second she could have a chance to, she'd take it. I'd do the same.