The 18-year-old, who made his first-team debut for the Tykes in April, has been a regular in Keith Hill's starting XI this season.
According to The Mirror, Moyes's scouts have frequently watched Stones over the past three months and the Toffees boss hopes to sign the youngster in January.
Stones, whose current contract expires in June 2015, has been capped twice by England at Under-19 level.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Wycombe WanderersWycombe | 13 | 9 | 2 | 2 | 31 | 16 | 15 | 29 |
| 2 | Birmingham CityBirmingham | 12 | 9 | 2 | 1 | 23 | 11 | 12 | 29 |
| 3 | Wrexham | 13 | 7 | 4 | 2 | 21 | 10 | 11 | 25 |
| 4 | Mansfield TownMansfield | 12 | 7 | 3 | 2 | 20 | 14 | 6 | 24 |
| 5 | Lincoln CityLincoln | 13 | 7 | 3 | 3 | 20 | 16 | 4 | 24 |
| 6 | Bolton WanderersBolton | 13 | 7 | 2 | 4 | 22 | 19 | 3 | 23 |
| 7 | Huddersfield TownHuddersfield | 13 | 7 | 1 | 5 | 19 | 12 | 7 | 22 |
| 8 | Barnsley | 13 | 6 | 4 | 3 | 21 | 18 | 3 | 22 |
| 9 | Reading | 13 | 7 | 1 | 5 | 21 | 20 | 1 | 22 |
| 10 | Stockport CountyStockport | 14 | 5 | 6 | 3 | 20 | 17 | 3 | 21 |
| 11 | Exeter CityExeter | 12 | 6 | 1 | 5 | 13 | 10 | 3 | 19 |
| 12 | Charlton AthleticCharlton | 13 | 5 | 4 | 4 | 15 | 14 | 1 | 19 |
| 13 | Peterborough UnitedPeterborough | 14 | 5 | 3 | 6 | 25 | 26 | -1 | 18 |
| 14 | Rotherham UnitedRotherham | 14 | 4 | 5 | 5 | 14 | 16 | -2 | 17 |
| 15 | Stevenage | 14 | 5 | 2 | 7 | 10 | 15 | -5 | 17 |
| 16 | Blackpool | 13 | 4 | 4 | 5 | 21 | 25 | -4 | 16 |
| 17 | Bristol Rovers | 13 | 5 | 1 | 7 | 15 | 20 | -5 | 16 |
| 18 | Northampton TownNorthampton | 13 | 4 | 3 | 6 | 17 | 20 | -3 | 15 |
| 19 | Wigan AthleticWigan | 13 | 3 | 5 | 5 | 12 | 11 | 1 | 14 |
| 20 | Leyton Orient | 13 | 3 | 2 | 8 | 11 | 18 | -7 | 11 |
| 21 | Crawley TownCrawley | 14 | 3 | 2 | 9 | 12 | 25 | -13 | 11 |
| 22 | Cambridge UnitedCambridge | 12 | 3 | 1 | 8 | 11 | 17 | -6 | 10 |
| 23 | Shrewsbury TownShrewsbury | 14 | 2 | 2 | 10 | 13 | 25 | -12 | 8 |
| 24 | Burton Albion | 13 | 0 | 5 | 8 | 13 | 25 | -12 | 5 |
| > League One Full Table | |||||||||
