The 25-year-old is currently on loan at Crotone from Sassuolo, where he is under contract until 2020 having signed an extension in January of last year.
He has caught the eye this term for the Serie A strugglers, scoring nine of their 23 league goals so far this term.
And now, according to reports in Italy, West Brom and Palace are keeping close tabs on his performances this season.
Since making his Sassuolo debut back in 2009, Falcinelli has been sent on a series of loan and has managed just 11 Serie A starts for the club.