Odemwingie fired the Super Eagles to their first win of the competition in Saturday's 1-0 victory over Bosnia-Herzegovina to boost their prospects of making the last 16.
The Stoke City ace feels that his nation are the sleeping giants of the tournament and claims that his teammates have the potential to reach the final at the Maracana on July 13.
"I saw a Brazilian on the street who told me he foresaw Nigeria playing the final against Brazil and I said to myself why not, going by the level of our players and the fact that they are yet to peak," Odemwingie told reporters.
"But mark my words - we have a very resilient defence, a creative midfield and an attack force that can trouble any defence in the world, if we played to our potentials, we can go all the way."
Second-placed Nigeria face already-qualified Argentina in their final Group F encounter on Wednesday knowing that a defeat would see them exit the competition if Iran beat Bosnia by a two-goal margin.