With his contract due to expire at the end of this season, Oxlade-Chamberlain was widely expected to leave the Reds on a free transfer this coming summer.
However, according to the Mails Sami Mokbel, who has had close links to the players camp in the past, there is a possibility that the Liverpool midfielder could depart this month.
Mokbel says Brighton have registered an interest in signing Oxlade-Chamberlain, but believes a deal hinges on whether Liverpool would allow him to leave for free this month.
Given the clubs current injury record, with just three senior forwards fit and available, that would seem unlikely for the time being.
But with Oxlade-Chamberlain a loyal servant to Liverpool for almost six years, if the 29-year-old is keen on a move to the Amex this month, there may be a possibility that Liverpool would allow him to leave for nothing.
Ridding his wages and freeing up a space in the squad could make even more sense if the club have their eye on another new signing before the close of the window.
Oxlade-Chamberlain missed a large chunk of the first half of the season with a hamstring problem, but returned to fitness in November and has made several starts since the resumption of Liverpools season last month.
He was, however, an unused substitute in Saturdays draw with Chelsea.
Speaking to Football Focus prior to that game, Oxlade-Chamberlain said he still feels he has plenty more to offer on the pitch in the coming years, and is keen for his son, who is almost two years old now, to remember his playing days:
A big motivation for me is trying to stay at a really good level for as long as possible, so that he can see me, he explained.
Obviously my Dad did it, but he did have me until he was 32. I didnt actually see him too often.
Im 29 now, hes nearly two, so he should be able to remember me. It gives you that bit of motivation to stay at that level.
When asked if he still had the same fire in him to impress on the pitch that he had at a younger age, Oxlade-Chamberlain said:
Theres a lot of competition for places, so when you do get the opportunity, it makes you that little bit more hungry to make sure you take it.
I still feel like theres more in me for sure.
Brighton, on paper, would be an ideal move for Oxlade-Chamberlain, allowing him to return to the south coast where he grew up.
Adam Lallana has enjoyed a positive spell with the Seagulls since leaving Anfield in July 2020, with Roberto De Zerbis side going from strength to strength in recent weeks.
If their interest in Oxlade-Chamberlain is genuine, it will be interesting to see if he plays any part in the Reds FA Cup fourth round tie at the Amex this Sunday.