Gazzetta dello Sport says Inter boss Antonio Conte is looking to strengthen his squad when the window opens and president Steven Zhang is willing to fund four major transfers to the tune of €130m.
Both have featured for Blues manager Frank Lampard this season but the 41-year-old has not settled on one or the other and is now exploring the market himself for a new left-back.
Alonso, 29, has made 20 appearances this season, while 25-year-old Emerson has played in 18 games.
The report claims that while Inter are interested in both, Conte prefers Palmieri because of his age and flexibility.
However, one plus for Inter is that both players have previous experience of playing in Serie A.