The Hammers offered Posh the chance to sign Oxford back in January, as Martin Samuelsen’s loan at the ABAX Stadium has been so successful.
However, the League One club decided against against signing the England youth international, as they didn’t want to sign him, just to put him on their substitutes’ bench.
“He’s a terrific young player, but we didn’t want to upset West Ham,” MacAnthony said during a question and answer session last night on Periscope.
“He has to play, if we have him. We couldn’t guarantee that.
“It didn’t affect our relationship with West Ham, as they appreciated we were honest with them. Reece Oxford knows we think he’s a class player.”
Posh currently have the likes of Michael Bostwick, Gabriel Zakuani, Jack Baldwin and Ricardo Santos competing for a place at centre back.
The quartet have all had a sizeable amount of action this season, with Graham Westley yet to settle upon a defensive pairing throughout his time in charge.
Oxford has generally impressed whenever given a chance at West Ham, but he has only played twice in 2016.
The 17-year-old’s most notable impact came earlier in the season, when he started against Arsenal at the Emirates Stadium, and put in a brilliant performance as the Hammers won 2-0.
After Peterborough’s rejection, West Ham did line him up with a loan move to Charlton Athletic in January, but that move fell through at the last minute.