Brown tells Liverpool to up bid for Tiger Turner
The 25-year-old is said to be keen on a move to Merseyside but Tigers boss Phil Brown wants more money on the table.
Turner had an impressive season as City narrowly managed to avoid relegation last season.
With Sami Hyypia's departure and injury concerns over Daniel Agger, Martin Skrtel and Jamie Carragher's fitness, Benitez is looking to spend some of the money he received from the sale of Xabi Alonso.
But the Liverpool boss will have to pay more than he wants if Turner is to join the club.
Brown said: "I have spoken to Rafa Benitez about Michael, but his assessment and valuation of the boy is well below ours.
"I would dearly love to keep Michael here with us, but I know that is going to be difficult.
"When one of the top clubs in Europe come calling, a young man's head can be turned."
Brown also revealed the club are close to completing a deal for Henri Camara, who is a free agent after being released by Wigan.
Brown said: "If we can sit down and thrash out a deal, then there's a possibility he could be a Hull City player. I'm sure we'll do that in the next 48 hours."