The London Evening Standard says Redknapp is a huge admirer of the defender, who he brought through West Ham's Academy into the first team when he was in charge at Upton Park.
Redknapp tried to sign the 32-year-old 12 months ago only to be told he wasn't for sale.
At the time he confessed he wasn't confident of ever signing Ferdinand but United now have six centre-backs at the club following the arrival of Blackburn defender Phil Jones, who Spurs were also interested in.
Redknapp said in April: "I've told the chairman many times that it's not always about the best players, it's about getting characters.
"Chelsea and United have had it over the years. William [Gallas] has given us experience and we've got Michael [Dawson] at the back but to keep progressing you need leaders. You can't have too many at your club."
Wages could be a stumbling block to any deal with Ferdinand earning £120,000 a week. But Redknapp needs help in defence with Ledley King and Jonathan Woodgate both having had injury problems.