Southampton have offered a fee in the region of £3.5million for the Republic of Ireland international with two Saints players also involved as part of a swap deal.
The South coast club are claiming that long time admirers, Tottenham Hotspur, remain favourites for Reids sigature.
I fForest are to cash in on one of their prize assets before the summer then any deal will have to be concluded by 5pm Monday when the transfer window closes.