The 31-year-old has been branded “wholly unprofessional” by the Baggies after being refused entry to Queens Park Rangers’ Loftus Road, when he believed a move had already been agreed.
To add to Odemwingie’s woe, events were captured by waiting television crews, but Redknapp insists it was an honest mistake.
“Let’s hope people give him an opportunity,” said Redknapp. “Show me someone who hasn’t made a mistake in their life, and I’ll show you liar.”
“There are people who are playing football that have made massive mistakes in their lives and they’re now back playing football.
“Odemwingie deserves a chance. He’s a good player and a good person.”
A possible move for the striker had been muted for several weeks, according to Redknapp, who regrets how the transfer had “dragged on”.
However, the R’s boss distanced himself from the saga by saying the board are responsible for any transfers.
“It shouldn’t come to the last day (of the January window), it’s the last thing I wanted to do,” added the 65-year-old.
“I wish the deal had been done three weeks ago and I could have been sitting with my family. I’ve not been involved in that for the last few years.”
QPR secured the services of three players – Chris Samba, Jermaine Jenas and Andros Townsend – on Thursday to cap off a successful January window, which saw Loic Remy and Yun Suk-Young also arrive.
ENHANCED ODDS: Get 8/1 on Arsenal to beat Man Utd - or 16/1 on Man Utd