Odemwingie took to Twitter over the weekend to hit out at West Brom and their fans, who had criticised him for requesting to leave the Hawthorns amid interest from Redknapp's Rangers.
And speaking after West Brom announced they had turned down a second bid for the Nigeria international, Redknapp told a press conference: "I don't know (whether the transfer will go ahead). It's a bit of a difficult situation for West Brom. It's not worked out in an ideal way. The whole situation has become a bit too public really hasn't it?"
He continued: "I am sure West Brom are not too happy with the way it's gone. We made an enquiry. The enquiry leaked out and obviously the player decided he wanted to come to London and that's how it has worked out.
"I think too many people get involved in Twitter."
Rangers had an initial £2million bid turned down at the start of the January window, and it was confirmed by the midlands club on Monday that a second offer has also been rejected.
West Brom's sporting and technical director (designate) Richard Garlick said in a statement: "QPR have made a second, improved offer for Peter, which we have turned down.
"As we have repeatedly stated, we have no need or desire to sell our core players.
"Since we turned down Peter's transfer request, he has made his position clear in a statement to the media and via his personal Twitter account.
"This matter will be dealt with internally."