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.
His actions appear to have harmed, rather than helped, his chances of leaving the midlands club.
West Brom are understood to be considering fining the 31-year-old, and Redknapp cast doubt on whether a move for the striker would go ahead.
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?
"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."