The 26-year-old had to leave the Republic of Ireland setup in order to travel to Humberside for a medical and talks with the Tigers, only for the deal to collapse late in the day.
Baggies boss Clarke has now held talks with Long, who is out of contract at the end of the season, and hopes that the former Reading striker will put pen to paper on a new deal at The Hawthorns.
"The club made a decision which was right for them – obviously I'm part of the club – but very quickly the bid collapsed," The Mirror quotes the Scottish coach as saying.
"Shane and his advisor need to sit down and talk with the club to try and get a resolution. Given contract talks had stalled for so long, it is possible that's why the club originally accepted the bid.
"Shane is a very, very important member of our squad. I'm delighted he's here."
Long scored 11 goals in 36 appearances in all competitions last season.