The 33-year-old has been contacted by Moore, who described him today as: “Someone who can lead the line well and knows how to score goals.”
Crewe who have been relegated from the Championship, are also in the running for Taylor as he ended last season on loan at Gresty Road.
His well-travelled career took off at Bristol Rovers and has included spells with Crystal Palace, Sheffield United and Manchester City.
Taylor also played for Port Vale and QPR on loan before Forest splashed out £500,000 to take him from Burnley.
The 6ft 2in target man was dropped midway through last season when Forest, who were struggling at the time, paid almost £1million for a new strikeforce.
He then scored four times in 15 games for Crewe, reaching a century of league goals along the way.
Taylor is also a Welsh international and was playing for his country as recently as season 2004/05.
Moore confirmed: “He's the kind of striker we're looking for, so I've registered our interest.”
Taylor has already been offered a contract at Crewe with a 12-month deal on the table — but it seems he would prefer the security of a longer contract.