Both clubs have asked the Premier League for permission to complete the deal this weekend.
City claim they did not have enough time to seal the switch after Benjani arrived late for his medical on Thursday.
But Pompey say City failed to fax over a document in time.
Redknapp said: "We both sent through forms at the same time. I think there was a minute to spare.
"The next thing I know is we get a call at about 12.30 saying all the forms didn't arrive.
"We were OK our end but for some reason some of his forms hadn't gone through."