Delph and Elliott are only 17 but have already featured in the Leeds first team, while England U16 player Garbett, 15, is at the academy.
The news will anger Leeds owner Ken Bates, who will not want to see his players leave on the cheap.
Newcastle will look to snatch the trio for a total of £1m, with the fees increasing over time if they reach the first team.
Toon owner Mike Ashley wants to build his club's youth policy but it will not be easy to convince Bates to sell.
Delph played in yesterday's 2-2 draw against Bristol Rovers.