After an exceptional debut season in the Premier League Turner has attracted the interest of Liverpool, Fulham and Everton but Redknapp is confident that the offer of first team football, which would not be guaranteed at Anfield, will facilitate a deal.
Tottenham are prepared to offer one or more squad players as well as £8 million cash, according to a report in the Mirror.
Hull manager Phil Brown would be reluctant to see one of his key men leave the KC Stadium but with Pascal Chimbonda likely to be included in the deal the money to spend in other areas would be tempting.
Fulham courted Turner earlier this month but the player would be reluctant to make what he believed would be a “sideways move” at this stage in his career.
Liverpool remain interested but have yet to make a serious move while Everton, who face the prospect of losing Joleon Lescott to Manchester City, would be unlikely to be willing to meet the asking price.
Meanwhile, Redknapp is still interested in bringing former Arsenal captain Patrick Viera to the club from Inter Milan despite admitting that the deal had “gone very quiet”.
“There’s been no progress whatsoever,” Redknapp said. “Vieira was a player I was interested in and he would bring something to this club.
“Whether it happens now I am not sure but I am certainly interested if he is available.”