The 22-year-old winger, who is a free agent after leaving Blackpool at the end of last season, spent Tuesday morning at the Premier League club.
Ince has attracted interest from a number of clubs since leaving Blackpool and travelled to Italy last month to discuss a possible move to Inter Milan, but decided to remain in England and was linked with a switch to Premier League newcomers QPR.
He spent a brief loan spell at Crystal Palace last season, scoring one goal in five appearances, and could gain more top-flight experience with the Tigers, who have been active in the transfer market ahead of the new campaign.
Jake Livermore joined on a permanent basis last month and Tigers boss Steve Bruce also landed Robert Snodgrass from Norwich for a fee thought to be around £7m.
Ince's contract at Blackpool has expired, but the Seasiders will still receive compensation because he is under 23.
Ince told Sky Sports News: "(The talks) were very positive. It's still ongoing but that's the first day of talks, so yes it has all gone well. We will see where it goes in the next couple of days.
"They (Hull) have brought in some good players, Robert Snodgrass being the latest one - a fantastic player who showed what he can do in the Premier League last year.
"I've been having a good look around, the facilities and the way they want to go with the club is forward and I'm sure they are going in the right stead with the right backroom staff.
"Steve Bruce has been absolutely fantastic for this club. The club is looking to go forward and it looks like they are bringing in the right type of players to do that."