The Baggies continued their fine start to the season by securing a last-gasp victory at Peterborough on Saturday.
But ahead of the transfer window closing on Tuesday, it is understood Albion are weighing up a move for Deeney who is set to leave Watford.
The 33-year-old came close to joining the Baggies last season with Deeney an alternative option if the club failed to complete a move for Karlan Grant.
The Express & Star understands Deeney was actually given a tour of Albion's training ground 12 months ago ahead of the proposed move.
But the Baggies then managed to agree a deal with Huddersfield for Grant – who subsequently put pen to paper on a six year deal at The Hawthorns.
Born in Birmingham, Deeney is a boyhood Blues fan and has held talks about a potential move to St Andrew's.
A host of other clubs are also believed to be interested in the former Walsall man who is now believed to be assessing his options.
On Friday, Watford released a statement explaining Deeney is in discussions with the club over his future.
The Hornets stated they are "discussing the best options for both parties" amid reports linking their captain with a move.
The statement read: "Troy Deeney and senior Watford FC officials are currently discussing the best options for both parties for the season ahead.
"The striker has one year left on his current Hornets’ deal, and has featured twice from the bench so far this year during this, his 12th season at Vicarage Road.
"Given the significant mutual respect between the club captain and the Board, these discussions shall remain private and confidential."
Albion signed fellow striker Jordan Hugill on loan from Norwich last week – with the 29-year-old making an impact from the bench at London Road.
Midfielder Jayson Molumby then became Ismael's sixth signing of the summer transfer window on Friday.
But speaking after the win at Peterborough, Ismael didn't rule out making another addition before the transfer window closes on Tuesday.
"I think we need to assess the squad after Peterborough with all the injuries," the Frenchman said when asked if Albion could add another player before the window closes.
"We have got a lot of players coming back after the international break.
"As I have said, we are still aware.
"But at the minute the last push we wanted we made with Jayson (Molumby). Now we need to assess all the players, the injured players, and then we will make our decision."
As well as potentially making a move for Deeney, Albion are believed to be trying to offload striker Kenneth Zohore before the window closes.