Tigers boss Steve Bruce missed out on the Republic of Ireland international striker on transfer deadline day in early September when a proposed £5million switch fell through.
Bruce has admitted he would "love" the opportunity to have another attempt at signing Long, who has scored three goals in 10 Premier League starts so far this season, and has also made four appearances from the bench.
However, the 26-year-old - whose Hawthorns contract is due to expire at the end of the season - is still highly thought of at Albion.
Downing admits there is uncertainty due to the managerial situation at the club, but is optimistic the former Reading ace, who has also been linked with Nottingham Forest, will put pen to paper at West Brom again.
"We are treating it that Shane is very much part of the set-up here," Downing told the Daily Star.
"The club are actively trying to get him to sign a new deal and we're quite confident of keeping him."