Noble, 20, came up through The Hammers youth system and has developed a regular enough spot in the side. He has made 43 league appearances for the Londoners netting 3 times in the process.
The England U 21 international is thought to be a target of Gordon Strachan this January and I wouldn't be surprised if the West Ham number 16 was slightly attracted by the move with the prospect of Champions League football at Celtic Park.
Personally I think that he would be an extremely good signing for the Hoops and that the European football would give Noble good experience for a possible England call up in the future.