The 29-year-old, who played under Joe Kinnear during his time at Wimbledon, would have to take a substantial pay-cut to join the Reds but would relish the chance to link up with his former boss.
I understand the deal would have already been completed had Celtic manager Martin O'Neill managed to secure a deal for Mark Viduka or Jimmy Floyd Hasselbaink but they both decided to sign for Middlebrough instead.
The Welsh international would add plenty to the current Forest strikeforce of Marlon King, David Johnson and Gareth Taylor and would perfectly fit the 'big name signing' bill that both Kinnear and Doughty have talked about in the past.
Talks have been put on hold until Celtic can find a striker to replace Henrik Larsson but Kinnear is likely to follow-up his interest when he returns from the pre-season tour in the USA.