Afobe spent the recently concluded season on loan at Millwall and made an impression as he hit the back of the net 12 times in the Championship.
The Stoke man was in a rich vein of form towards the end of the campaign as he grabbed six goals in his final nine league outings.
Afobe is attracting interest from Watford, who are looking to bounce back up to the Premier League, and are claimed to want to snap him up.
Millwall though are hopeful they can win the race for Afobe and take him back to the Den on a fresh loan agreement.
The London outfit are also moving to try to bring in midfielder Lewis Ferguson from Aberdeen and have put a bid of £1.5m in for the player.
They have also offered fresh terms to winger Jed Wallace.
Millwall finished ninth in the Championship last season, missing out on a spot in the playoffs by six points.