This represents both nations' third appearance at the finals, and neither have managed to progress past the pool stage before.
However, although Colombia are already assured of a top-two finish in Group C, Greece and Ivory Coast both have a chance of making history in Brazil.
The African country are in the driving seat to do just that, as they sit second in the pool after taking three points from their first two fixtures.
Sabri Lamouchi's side came from behind to beat Japan 2-1 in their opening game before going down by the same scoreline to Colombia last Thursday.
That means they could progress with just a draw at Estadio Castelao, as long as Japan do not beat Colombia in Cuiaba.
Greece, meanwhile, have just a point to show from their first two matches, meaning the equation is simple for them - they must win in Fortaleza to stand any chance of going through.
However, Fernando Santos' side will need to be much more clinical than they have been so far, with the European outfit yet to score in the tournament.
Santos' men were well beaten by Colombia in their opener, but kept their dreams of reaching the last 16 alive by claiming a 0-0 stalemate with Japan.
Captain Konstantinos Katsouranis was sent off seven minutes before half-time in that game, though, meaning he will miss this match through suspension.
Much was expected of Ivory Coast ahead of the tournament with Yaya Toure in midfield and Didier Drogba in attack.
But Toure has struggled to make an impact so far, while talismanic striker Drogba has had to settle for substitute appearances in both games.
Lamouchi may turn to Drogba, his country's all-time leading goalscorer, for inspiration on Tuesday, although the former Chelsea man will have to get the better of one of Europe's meanest defences if he is to score his third World Cup finals goal.
Greece conceded just four goals in their 10 qualification games before beating Romania 4-2 in a play-off to reach Brazil.
