The 31-year-old Italy international was a target for the Baggies in January and almost completed a move on deadline day before the Italian giants pulled the plug at the last minute.
But he is now surplus to requirements at The Old Lady and has been told he leave the club this summer.
And West Brom are weighing up a potential return for Udinese and Napoli striker, although they will have to fight off interest from Serie A sides Lazio and Samprdoria.
Quagliarella arrived at Juventus in a €10.5million move from Napoli in 2010, but injuries have since halted his progress at the club.
The experienced striker has also been capped 25 times by Italy.