Having learned of his club's refusal to sell him, 31-year-old Odemwingie then went public to voice his unhappiness at their decision on the social networking site Twitter.
Reflecting on the current situation, Redknapp has conceded that it "has become a bit too public" for his liking.
"I don't know [if the transfer will go ahead]. It's a bit of a difficult situation for West Brom," he told reporters. "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."
The deadline for transfers to be completed will pass at 11pm this coming Thursday.