Albion boss Paul Peschisolido has publicly expressed his interest in the 27-year-old, who has been told he is free to leave the club.
Elding is talking to several clubs and Crewe caretaker manager Dario Gradi believes something could materialise shortly.
"Anthony is free to talk to other clubs and I know he is doing that. Therefore, something could happen with him before the weekend," Gradi told the club's official website.
"If it is a loan with a view to a permanent deal then that is something we would also consider. At the moment we can only loan him out until January, so that is what we will look to do."