Bogdan has spent the last two campaigns at Anfield but he has failed to make any sort of an impact at the club, with just six appearances being made in all competitions.
The Hungarian stopper was loaned out to Wigan Athletic at the start of last season, but a serious knee injury brought an end to his time at the DW Stadium after 17 appearances in the Championship.
However, according to the Daily Mail, he will be given another opportunity to impress in the second tier with Forest head coach Mark Warburton keen to take him to the City Ground.
Bogdan is yet to return to full fitness, but it has been suggested that Warburton would like the 28-year-old to compete for the number-one jersey during the upcoming campaign.
Before joining Liverpool, Bogdan played 120 times in all competitions for Bolton Wanderers.