White has been out on loan twice at Conference side Dover Athletic in the last couple of years, having failed to break into the first-team picture at Priestfield.
Hessenthaler told the club's official website: "Ben came to see me because he wants regular first-team football.
"He's a young lad with a future, but perhaps not in Division One at this present time.
"But stranger things have happened and you never know. If he does well in the reserves he'll have a chance, but we've said we'll help him to look for another club."