Tykes boss Gudjon Thordarson has been searching for defensive reinforcements after losing Peter Handyside and Lee Crooks to injuries.
Monk is well down the pecking order at Southampton and the club are willing to let him go out on loan for regular first team football.
Barnsley are hopeful of concluding a deal in the next 24 hours as they look to have Monk available for this weekend's clash with Bristol City.
Meanwhile, Barnsley have taken former Bolton ace Paul Warhurst on trial.
Warhurst is looking for a new club after being released by Chesterfield earlier this week and he will train at Oakwell in the hope of securing a move to the Yorkshire outfit.
