It was about a little girl who tells her mom about a strange alien that she and the other kids have found while playing. The mom is not interested and keeps cooking or doing other chores, while the daughter takes out all kinds of materials to rebuild a rocket or some sort of machine for the extraterrestrial. She repeats weird ideas that the alien has shared. It might have been by Asimov or Bradbury.
Your description sounds a lot like Ray Bradbury's classic short story "Zero Hour" which was also the answer to this old question. You can read it for free here or here, or listen to a radio dramatization here.
You didn't mention an invasion in your question, but you did use the alien-invasion tag. "Zero Hour" is the story of an invasion of our Earth from another dimension, using the small children of Earth as a Fifth Column. Following instructions from the aliens, small children all over the world are using common household objects to construct interdimensional portals for the invasion.
The story is focused on one housewife and her little girl Mink, who is the leader of the local band of tiny traitors. Mink tells her mother about the invasion, but the mother doesn't take it seriously until near the end.
Mink ran into the house, all dirt and sweat. For her seven years she was loud and strong and definite. Her mother, Mrs. Morris, hardly saw her as she yanked out drawers and rattled pans and tools into a large sack.
"Heavens, Mink, what's going on?"
"The most exciting game ever!" gasped Mink, pink-faced.
"Stop and get your breath," said the mother.
"No, I'm all right," gasped Mink. "Okay I take these things, Mom?"
"But don't dent them," said Mrs. Morris.
"Thank you, thank you!" cried Mink and boom! she was gone, like a rocket.
Mrs. Morris surveyed the fleeing tot. "What's the name of the game?"
"Invasion!" said Mink. The door slammed.
In every yard on the street children brought out knives and forks and pokers and old stove pipes and can openers.
Mink comes in for lunch and has this conversation:
"Slow down," said Mom.
"Can't," said Mink. "Drill's waiting for me."
"Who's Drill? What a peculiar name," said Mom.
"You don't know him," said Mink.
"A new boy in the neighborhood?" asked Mom.
"He's new all right," said Mink. She started on her second bowl.
"Which one is Drill?" asked Mom.
"He's around," said Mink evasively. "You'll make fun. Everybody pokes fun. Gee, Darn."
"Is Drill shy?"
"Yes. No. In a way. Gosh, Mom, I got to run if we want to have the Invasion!"
"Who's invading what?"
"Martians invading Earth—well, not exactly Martians. They're—I don't know. From up. She pointed with her spoon.
"And inside," said Mom, touching Mink's feverish brow.
"You're laughing! You'll kill Drill and everybody."
"I didn't mean to," said Mom. "Drill's a Martian?"
"No. He's—well—maybe from Jupiter or Saturn or Venus. Anyway, he's had a hard time."
"I imagine." Mrs. Morris hid her mouth behind her hand.
"They couldn't figure a way to attack Earth."
"We're impregnable," said Mom in mock-seriousness.
"That's the word Drill used! Impreg— That was the word, Mom."
"My, my. Drill's a brilliant little boy. Two-bit words."
"They couldn't figure a way to attack, Mom. Drill says—he says in order to make a good fight you got to have a new way of surprising people. That way you win. And he says also you got to have help from your enemy."
"A fifth column," said Mom.
"Yeah. That's what Drill said. And they couldn't figure a way to surprise Earth or get help."
"No wonder. We're pretty darn strong," laughed Mom, cleaning up. Mink sat there, staring at the table, seeing what she was talking about.
"Until one day," whispered Mink melodramatically, "they thought of children!"