Arsenal are already tracking the 17-year-old Spartak Moscow midfielder.
Spartak sporting director Dmitri Popov insists the club will not listen to offers till Ananidze is at least in his 20s.
"I read the stories," said Popov.
"The list of clubs did not surprise me, especially the first two: they are built on continually searching for new talent.
"But Spartak haven't received formal offers and we don't intend to consider them for the next three or four years."