Pellistri, who is 19, joined United last summer from Penarol in Uruguay.
He went out on loan in the January transfer window, after spending around six months with United's under-23 side.
After playing 12 times for Alaves, Pellistri has impressed enough for them to seek another loan.
Journalist Jonathan Shrager claims a full season loan is a possibility, with United happy to agree to a loan as it would further Pellistri's development.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!