Huddersfield hitman Grant remains their number one target with Watford duo Deeney and Gray alternatives.
But The Express & Star understands the Baggies are not pursuing a move for Bournemouth's Josh King who is believed to be seeking £90,000 per week – what the Cherries paid him in the Premier League.
It is believed the Terriers are asking for between £16million and £18million for Grant who scored 19 goals for them last season despite their struggles in the Championship.
With money tight at The Hawthorns, Albion are hoping to negotiate a deal that would see them initially sign the 23-year-old on loan.
The deal would then give Albion the option to purchase the player for a set-price at any time, or they would be obligated to buy him if they retain their Premier League status for a second year.
Head coach Slaven Bilic and sporting director Luke Dowling both see Grant as the final piece of the jigsaw for Albion this window.
At 23-years-old, the player will also have a significant resale value if he fulfils his undoubted potential at The Hawthorns.
It is understood Grant is eager to join Albion and has told Huddersfield's hierarchy he feels the time is right for him to move on.
And there is an acceptance from all parties that a deal is likely to be agreed with Huddersfield CEO Mark Devlin going on record this week to explain how the coronavirus pandemic has impacted the club.
"The current situation means we'll be approximately £3-4million worse off this season than had we had crowds and our corporate partners here," Devlin said.
"That's a huge hole even for a club that's benefitting from parachute payments and has effects right the way across the business."
If Albion can't strike a deal for Grant, however, Watford's Gray and Deeney have been lined up as alternatives.
It is understood both players have been made available by the Hornets.