This sounds like the 1994 miniseries, Red Planet, adapted from the 1949 Robert A. Heinlein novel of the same name.
According to the Wikipedia synopsis, a boy called Jim meets an alien called Willis on the distant mining world of New Aries. Toward the end of the story, Willis tells Jim that they'll have to part ways, as he needs to metamorphose to become an adult, and this will take a long time. Many decades later, Willis is now an adult, and friends with Jim's young granddaughter, to whom he tells stories of the adventures he and Jim had together.
And yes, Willis (when his body is curled up into a ball) does appear as a furry blob with tentacle legs, although he can also extend his body and stand upright on his hind legs.
Jim Marlowe (voiced by Benny Grant), Jr., and his little sister, Phillis Jane "P.J." Marlowe (voiced by Haven Hartman), are teens growing up on the distant mining world of New Aries. Life on New Aries is difficult, with its surface being a red-colored desert. Along with the harsh climate and severe weather, there are many dangerous creatures living on New Aries, such as the three-headed Cerebus Hounds, the swift and voracious Water Seekers, and the misunderstood Locals, creatures so rare and dangerous they border on urban legend.
Jim has recently acquired a new pet, a "roundhead" called Willis (voiced by Pat Fraley) with the parrot-like ability to mimic human speech and record conversations. Willis is small, furry, and playful, can survive both on the surface of New Aries and the Earth-like atmosphere of the colony, and has some sort of connection with the Locals on an almost empathic level.
As Jim and P.J. are about to be sent off to a boarding school, their mother (voiced by Marcia Mitzman Gaven), the colony's medical officer, discovers a substance deep within the mines that is killing the miners. The school's headmaster Marcus Howe (voiced by Roddy McDowall) and the colony leader (voiced by Nick Tate)—a company man from the Beta Earth Mining Company—learn of Jim Marlowe's new pet, and plot to steal him for medical experiment in order to generate a serum to protect the miners, and thus, keep the company in the black. Willis records this entire conversation, which prompts Jim, Willis, and P.J. to escape into the desert. With their life-support running low, they are forced to take shelter in a carnivorous plant, using the process of photosynthesis so the plant will generate oxygen and keep them alive.
Running from New Aries' many dangerous life-forms, they are eventually found by the Locals. They are enraged by the attempted capture of the tiny Willis. In the end, only Jim and Willis' friendship save the colony world from destruction by the angered natives, who reveal themselves to be an intelligent, highly advanced subterranean race.
Willis then tells Jim that it is time for him to go. He is finished being a child, and must become an adult via metamorphosis. One of the colony's doctors correctly assumed that Willis was not a separate species from the Locals, but rather a Local in its infant form. Jim says that he will wait for Willis to finish changing, but Willis states that this will take a long, long time. He and Jim will probably never see one another again.
Many decades later, New Aries has been terraformed into a green, Earth-like world, with humans and Locals living side by side in peace. Willis, now a full-grown Local, has befriended Jim's young granddaughter, and spends time with her wandering the grass-covered hills and telling her stories of the adventures he and her grandfather had together.