The Anfield chief has a number of injury worries in defence, which were compounded on Saturday when Jamie Carragher limped off early in the first half of the friendly with Atletico Madrid nursing an ankle problem.
Benitez is increasingly short of defenders, having seen Sami Hyypia and Alvaro Arbeloa leave the club this summer.
Benitez has been linked with a bid for Turner, as well as Portsmouth's Sylvain Distin.
And the Spaniard said after the 2-1 defeat by Atletico Madrid at Anfield: "I was talking with (Hull manager) Phil Brown, but I will not talk about figures. But maybe I was just talking to Phil about the weather."
Benitez is believed to have offered £6m for Turner, with Hull demanding closer to £12m.
On Liverpool's injury problems, which also saw Fernando Torres limp off at the end with an ankle injury, Benitez said: "Carragher twisted his ankle, and because we have problems with injuries to our centre-backs, we decided to take him off as a precaution.
"We will have to wait to see how the injured players improve, but I feel they will be ready for our next game.
"We have two options. One is to bring in someone at the back and the other option is to keep working with the young players we have.
"We have three centre-backs to get fit and will need one more as a fourth. We have to decide what to do, but the one solution we can achieve is to work with the youngsters.
"Some youngsters need the opportunity to impress, we will see how they go.
"Jamie will come in tomorrow for treatment at Melwood, and we will assess the situation then.
"For a twisted ankle you need two or three days to see how the injury settles down. I do not believe he will need a scan.
"Fernando Torres also came off with an slight injury on his ankle, but he also came off as a precaution because this was only a friendly."
Liverpool played most of the match with Spanish youngsters Danny Ayala and Mikel San Jose in central defence against the outstanding Atletico forward Sergio Aguero.
Benitez said: "It was difficult for the youngsters against players of such quality who keep possession and are very clever in offence."
Aguero, a target for Chelsea, scored one goal and created a second for Diego Forlan in the first half, with Lucas Leiva replying for Liverpool in the final minutes.
Atletico coach Abel Resino dismissed the Chelsea connection, saying: "As far as I know we have not had any bids for Aguero."