Widely regarded as one of the best players in the Championship, former Wolves man Wallace is set to become a free agent at the end of the current campaign.
With Millwall still in with an outside shot of making the play-offs, the Lions are hoping they can win promotion and keep Wallace at The Den.
But the right winger, who can also play as a number 10, is expected to move on this summer.
Wallace will arguably be the hottest free transfer on the market with Steve Bruce understood to be a big fan of the 28-year-old.
Nottingham Forest are long-term admirers of the former Portsmouth man and are likely to be serious contenders to land his signature.
Reports have also emerged that a host of clubs in Turkey are interested in the forward.
One of those clubs is said to be Besiktas, who are now managed by former Albion boss Valerien Ismael.
Those reports claimed Wallace is close to finalising a move abroad.
But the Express & Star understands the forward is yet to make a final decision on his future – with the 28-year-old keen to explore all his options at the end of the season.
Albion manager Steve Bruce is determined to overhaul his squad this summer. The boss has made it clear he wants to add more creative players to his ranks. He is also keen to exploit the free agent market.
The addition of Wallace would help transform Albion’s miss-firing front line.
And speaking after last week’s draw with Coventry, the boss confirmed the club is working to identify players who can improve Albion in the final third.
“We lack creativity, we have got no real pace in the top area or in the midfield area,” the boss said.
“We are a bit samey.
“We have been busy but every club will have been busy – if you are doing your job right you never stand still.
“We are looking at the lists of Bosman’s for example, who is out of contract. We’ve done our homework.”