Ibrox side Glasgow Rangers are linked with the 21-year-old.
The Daily Mail reported on Thursday that Rangers remain in talks about signing the Manchester City starlet.
Gerrard's side took a big step toward the third round of Europa League qualification last night by securing a 1-0 victory away to Croatian side Osijek in the first leg.
Speaking to The Record afterwards, the 38-year-old was guarded on his pursuit of the midfielder, but did admit an "interest".
“I’ve got nothing to say on it at the moment because he’s not our player, but there is an interest," he said.
If the move happens, Bryan will be the Blues' 11th summer signing under Gerrard - and the seventh player to arrive on a permanent deal.
The 21-year-old is ordinarily a box-to-box midfielder, but has successfully operated in a centre-back role in the past.
He's clearly a versatile talent and, given he's a midfielder at heart, it'll be interesting to see whether Gerrard, one of the best of his generation at one point, can bring his game to the next level.