The Blackburn right-back joined the Brewers in August and has been a virtual ever-present in manager Gary Rowett's starting XI, making 31 appearances in all competitions.
However, his current agreement is set to expire on January 12.
Rowett told Albion's official website: "Anthony has come in this season and performed really well, he's been one of the mainstays in the team over the first half of the season.
"Playing senior football is obviously a huge factor in his development and we've been speaking to Blackburn and we're close to finalising a deal to keep him with us until the end of the season."
O'Connor's arrival has seen fellow right-back Andy Corbett struggle for opportunities this season and he has now joined Blue Square Bet Premier side Hereford on a one-month loan deal.
Meanwhile, Burton goalkeeper Stuart Tomlinson has penned a new one-month contract at the Pirelli Stadium which runs until the start of February.
Tomlinson is continuing to step up his fitness having suffered a cruciate ligament injury in October. Rowett added: "We are really pleased that Tomo is ahead of schedule in his recovery and we've always wanted to support him through the injury.
"We see him as part of the squad and the very second that he's back fit we will look at doing something longer. This extension allows some more time for him to get back to fitness."
