Odemwingie laughs like everyone else when asked if West Brom can qualify for the Champions League this season.
But then he remembers how people did the same when he joined French club Lille eight years ago and turned a similar fantasy into reality.
The Nigeria striker, 31, told The Sun: "At Lille nobody expected us to qualify for any European competition.
"We didn't even have any bonuses in our contracts for getting into the Champions League because it seemed pointless to write it in.
"But we shocked everyone by finishing second in the table behind Lyon to qualify.
"Lille are a properly established European club now but what they achieved then was amazing at the time, a real dream - and it shows that all things are possible in football.
"To be honest, I don't even know if there are Champions League bonuses in the West Brom contracts. We know it's unlikely we will be in the same position at the end of the season but I always have the experience at Lille in the back of my mind."