Crewe are leaving for a pre-season tour of Malta without Smith and manager Dario Grady will now look for a new left-back, and captain.
Tigers manager Jan Molby said: "Shaun Smith said he is keen to join Hull City, but he wants to consider one or two other options he has received.
"He was at the club again yesterday and I know he is impressed with what we have to offer which hopefully will persuade him to sign for us. All we can do now is wait for him to get back in touch with us."
News in Brief
The £230,000 purchase of Motherwell's Stuart Elliott is still on course to be completed tomorrow.
City are coming through pre-season training with a clean bill of health. There do not appear to be any injuries ahead of the first friendly at Lincoln United on Monday.
Hull City are looking for any supporters who will be available on Wednesday to help protest against former ITV Digital owners Granada and Carlton. There is a free coach, with refreshments, going down to the London offices of the two media giants, before returning to Yorkshire in time for City's friendly at Bradford Park Avenue in the evening (free entrance). If you are interested, contact Fans' Liaison Officer Dan Prant by phone (01482 501427) or e-mail (danielp@flo.hulltigers.com).
Adrian Caceres is on trial with Bournemouth, and scored in a friendly match for the Cherries. The 21-year-old made 4 appearances for City at the end of last season.
Carlisle United have dismissed rumours linking their star forward Richie Foran with a move to City. A spokesman said: "It is absolutely not true. We have not received any bids for Richie Foran.
"He returned to pre-season training last week with the rest of the players and he's going nowhere."