The Nigeria international was part of the Baggies team that shocked the Premier League by reaching third spot before a run of one point from four games hampered their progress.
But the 31-year-old forward feels Albion can be a real force under Steve Clarke and claims an impressive finish is not beyond them.
"When a new manager comes in there is uncertainty but things are going well," said Odemwingie.
"Our points total is based on our performances not on dreams and the manager has been very quick to settle us down.
"The fans are excited and loving the quality of football we are producing at the moment.
"There is nothing wrong with those dreams we have of finishing in the top five.
"Maybe we can continue with that and see how far we can go. There is no doubt we will do better than last season.
"We've had an exceptional start to this campaign and we are hoping for an exceptional end."
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