The Stoke City forward scored the only goal of the game against Bosnia-Herzegovina on Saturday to put Nigeria on the verge of qualifying for the last 16 in Brazil.
Odemwingie believes Nigeria have what it takes to go all the way to the final and the 32-year-old revealed that he is not the only one who is optimistic about their chances.
"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," he said.
"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."
The African champions only need a point against Argentina at Estadio Beira-Rio on Wednesday to ensure they will progress from Group F along with their opponents, and they will also be guaranteed to go through if Iran fail to beat Bosnia-Herzegovina.
Nigeria have not featured beyond the group stage of a World Cup since 1998.