Oxlade-Chamberlain came through the ranks at Saints before earning a move to Arsenal, and reports have suggested that the club would like to take him back on loan.
What should Liverpool do with Oxlade-Chamberlain this summer?
However, Liverpool have trimmed their squad throughout the transfer window and have allowed a number of fringe players to leave the club.
Harry Wilson has moved to Fulham, Taiwo Awoniyi has moved to Union Berlin, and Xherdan Shaqiri has moved to Lyon in deals that have netted Liverpool transfer fees.
They have also let Marko Grujic, Ben Davies, and Ben Woodburn leave on loan, to Porto, Sheffield United, and Hearts respectively, and Georginio Wijnaldum has gone to PSG on a free transfer.
With Ibrahima Konate being their only first-team signing of the summer, Jemson insists that it makes no sense to allow Oxlade-Chamberlain to leave before the deadline.
He told This Is Futbol: “I just don’t see him going. You talk about Shaqiri going, someone like that, you can’t let three or four of your squad players go. How do you bring the same sort of quality in with the money they’re talking about them going for?
“It’s not good business that, for me, so I’d be very, very surprised to see him go.”