Jones, who was released by Liverpool at the end of last season after five years with the club, was initially linked with the Baggies - but it's now Forest boss Dougie Freedman who is showing the keenest interest.
It's understood Jones, 33, is in discussions over a two-year contract at the City Ground as Freedman looks for a keeper to provide competition for the club's current first choice, experienced Dutchman Dorus de Vries.
Jones made 26 appearances at Anfield where he was back-up to first Pepe Reina and then Simon Mignolet after signing for the Reds from Middlesbrough in 2010.
Forest, which sacked former England international Stuart Pearce in February, finished 14th in the Championship last season after falling away badly after a promising start to the campaign
The team, whose back-to-back European Cup wins in the late '70s under colourful coach Brian Clough are the stuff of legend, is owned by Kuwaiti businessman Fawaz Al-Hasawi, who has vowed to lead Forest back to the top flight.
It was last relegated from the Premier League in 1999, and even fell into League One six years later, before returning to the Championship - where it has lingered since.
Jones, who has four Socceroos caps, has been holidaying in the Maldives with his fiancée, Dani Lawrence, with the couple due to marry in the coming months.
