Bailey is Jamaican and has represented the country at youth level, but he is eligible to play for England because two of his grandparents hold British passports.
"Well, I'd have to say until a few months ago we had no indication that he was eligible for England," Southgate told 'BBC Radio5Live'.
"That's still a process that is ongoing and now that issue has been flagged, he's somebody we'll monitor more closely.
"But that's more for our talent identification department at this stage than it is for my selection in the short term."
Bailey has scored nine goals and provided five assists this season as Leverkusen look to qualify for the Champions League.