Cort Is Taylor's First Choice
He told the Hull Daily Mail: "I'm hopeful Leon Cort will come up to talk to us in the middle of next week.
"I am interested in Ben, but he would require a fee and Leon doesn't. That's one of the reasons I've gone down the road with Leon.
"They're both very, very good players."
Taylor also gave a clear indication that adding another defender to his squad will not mean the end of Justin Whittle's 5-year spell at the club. The 32-year-old is out of contract but looks set to stay for at least another season.
The City boss said: "I think the defence did well last season apart from a couple of individual mistakes.
"However, if we can add to it with another player then he will be there to push Damien Delaney, Marc Joseph and Justin Whittle all the way.
"It will only improve us if we can get a player like Leon."