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 | Wrexham | 6 | 4 | 1 | 1 | 12 | 5 | 7 | 13 |
| 2 | Birmingham CityBirmingham | 5 | 4 | 1 | 0 | 11 | 6 | 5 | 13 |
| 3 | Charlton AthleticCharlton | 6 | 4 | 1 | 1 | 6 | 3 | 3 | 13 |
| 4 | Huddersfield TownHuddersfield | 5 | 4 | 0 | 1 | 10 | 3 | 7 | 12 |
| 5 | Stockport CountyStockport | 5 | 3 | 2 | 0 | 9 | 2 | 7 | 11 |
| 6 | Lincoln CityLincoln | 5 | 3 | 1 | 1 | 10 | 6 | 4 | 10 |
| 7 | Barnsley | 6 | 3 | 1 | 2 | 10 | 9 | 1 | 10 |
| 8 | Mansfield TownMansfield | 5 | 2 | 2 | 1 | 9 | 10 | -1 | 8 |
| 9 | Stevenage | 5 | 2 | 1 | 2 | 5 | 3 | 2 | 7 |
| 10 | Wycombe WanderersWycombe | 5 | 2 | 1 | 2 | 10 | 9 | 1 | 7 |
| 11 | Peterborough UnitedPeterborough | 5 | 2 | 1 | 2 | 7 | 7 | 0 | 7 |
| 12 | Reading | 5 | 2 | 1 | 2 | 5 | 5 | 0 | 7 |
| 13 | Crawley TownCrawley | 5 | 2 | 1 | 2 | 4 | 6 | -2 | 7 |
| 14 | Bristol Rovers | 6 | 2 | 1 | 3 | 4 | 8 | -4 | 7 |
| 15 | Wigan AthleticWigan | 5 | 2 | 0 | 3 | 6 | 5 | 1 | 6 |
| 16 | Exeter CityExeter | 5 | 2 | 0 | 3 | 6 | 6 | 0 | 6 |
| 17 | Rotherham UnitedRotherham | 6 | 1 | 3 | 2 | 5 | 7 | -2 | 6 |
| 18 | Northampton TownNorthampton | 5 | 1 | 2 | 2 | 5 | 6 | -1 | 5 |
| 19 | Blackpool | 5 | 1 | 2 | 2 | 9 | 12 | -3 | 5 |
| 20 | Burton Albion | 5 | 0 | 4 | 1 | 7 | 8 | -1 | 4 |
| 21 | Bolton WanderersBolton | 5 | 1 | 1 | 3 | 2 | 9 | -7 | 4 |
| 22 | Leyton Orient | 5 | 1 | 0 | 4 | 3 | 8 | -5 | 3 |
| 23 | Shrewsbury TownShrewsbury | 6 | 1 | 0 | 5 | 4 | 10 | -6 | 3 |
| 24 | Cambridge UnitedCambridge | 5 | 0 | 1 | 4 | 5 | 11 | -6 | 1 |
| > League One Full Table | |||||||||
