Gibson has recently been in Spain with Newcastle’s senior squad, and he played a part a part in their friendly victory against Lillestrom earlier in the week.
It has been suggested on the club’s site that Gibson has impressed Steve McClaren while training with the senior squad, and Beardsley continued to praise the 18-year-old today.
"He's a great kid," he said. "He's got a lovely left foot, he's strong, physical, can run and he has a good understanding of the game.
"The only thing he's maybe lacking is confidence. I don't think he realises what he has, because he has a lot of strengths, a lot of positives, and I just wish sometimes he would believe in himself a bit more. He's certainly got the talent."
Gibson is yet to make his competitive debut for Newcastle, but he was included on the bench against West Bromwich Albion earlier this month.
The youngster is pushing for a first-team place, but his resurgence has not gone entirely unnoticed.
According to a report on TeamTalk, former Newcastle boss Alan Pardew has been alerted to Gibson’s progress, and he is now weighing up whether to make a move to try and bring the starlet to Crystal Palace with him.
Gibson’s contract at Newcastle expires in the summer, and he is yet to sign progressional terms with the Tyneside's, meaning that his future remains in doubt, despite his recent emergence.