Palestra is currently on-loan at Cagliari this season, where his form has impressed watching scouts.
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Italian transfer expert Nicolo Schira is reporting Newcastle and Tottenham are preparing offers for Palestra this summer.
The youngster is also on Inter Milan's shopping list.
Palestra came through the Atalanta youth system and while uncapped at senior level, he has been called up to Italy's squad this season at 20 years of age.