West Brom have accused the 31-year-old striker of acting in a "wholly unprofessional" manner by driving to talk terms with Rangers despite no deal having being agreed between the clubs.
But the Nigerian international claims that he had an understanding with Baggies technical director Dan Ashworth that he could drive to London with a view to the clubs reaching an agreement.
"They didn't give me written permission but we are in England and when you are gentlemen you understand each other easily," Odemwingie, who was sent home from training on Friday morning, told Sky Sports News.
"I had to be in training that morning but when that was done I asked if I could go as I had to pack and start driving. I got the go-ahead from him (Ashworth) as far as I understand so I went round and said goodbye to everyone and thank you. In my opinion everything was done right. He can deny it because he has to look good in this situation.
"I knew that it took two hours to drive to London and I had to be there because we were 90% there and then the deal didn't happen. We were almost there, the club were angry that I went there and it was on TV. They weren't angry that I went there, but when it came up on TV that's when they said that this deal is off and asked why did I did it.
"My only regret is that I didn't have the paper in my hand before I went to London."
While admitting that his actions had been "a bit unprofessional", he also claimed the circumstances were not that different to those that saw him sign for West Brom from Lokomotiv Moscow.
"I came to this club (West Brom) in a wholly unprofessional way," he said. "I wasn't given any written permission by Lokomotiv Moscow but I arrived at this club. I did a medical, I don't think everything went so professional when I arrived."
The club confirmed on Friday that while preliminary discussions over the saga had been "constructive," Odemwingie had been given permission to return home and will play no part in Sunday's home clash with Tottenham.
Odemwingie, who has 18 months left on his West Brom contract, confirmed that he still wishes to leave the club for personal reasons.
"I believe if West Brom brought me back here it is because they believe there is a way I can be back on the pitch and giving my best to the team," he said.
"I will always love the club but I will still leave, it is just a matter of time. I understand the need to honour your contract but the club have known the reasons I want to leave for some time now. They feel I can overcome that, but they don't know my heart.
"My contract runs out in a year and a half. I wasn't offered an extension here. My career ends one day and so will my contract here at West Brom."
Speaking later outside the club's training ground, Odemwingie said: "I've had a chat with Dan Ashworth this morning and the club will say more later.
"I have been given a few days off and will be back in training next week."
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