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 when you are gentlemen you understand each other easily," said Odemwingie.
"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. My only regret is that I didn't have the paper in my hand before I went to London."
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."
West Brom later confirmed that Odemwingie would not be involved in Sunday's home game with Tottenham.
A club statement read: "Albion confirm that Peter Odemwingie reported for training this morning.
"The player met with board members Dan Ashworth and Richard Garlick and head coach Steve Clarke for preliminary discussions which proved constructive.
"After the events of the past week, the club decided it is in the best interests of all parties that Peter is not involved in Sunday's game and he has been given permission to return home."