The 19-year-old has returned to the London club after spending last season on loan at Borussia Monchengladbach.
Pellegrini initially wanted to keep the youngster but the Hammers boss is now looking to secure for Oxford another temporary switch.
With that in mind, Celtic should move quickly and try to secure a loan move for him before the end of this month.
Signing a defender is a priority for Brendan Rodgers, and Oxford could be a smart signing for the club.
The highly rated youngster has managed to make 17 appearances for the Hammers since breaking into the senior team from the club’s academy in 2015.
Oxford is a versatile young player who can play at centre-back or in central midfield which means he can be a utility player for the Scottish champions.
While Celtic have been linked with a move for Scott McKenna, Aberdeen’s asking price for the Scot defender is a real put off.
Instead, Rodgers should look to sign a player like Oxford who has shown his potential and class while playing both in England and abroad.