The nations won their respective opening matches on Saturday and another victory for either would all but secure their place in the knockout stages.
In a group where all four sides will have had high expectations of qualification when the tournament began, Colombia and Ivory Coast struck first as they triumphed over Greece and Japan respectively.
Jose Pekerman's team were in particularly impressive form as they swept aside the Greeks 3-0 while Sabri Lamouchi's men came from behind to beat Japan 2-1.
Ivory Coast started slowly in their opening clash and a repeat could cost them against a Colombia side who were ahead inside six minutes in their first game.
The return of Fredy Guarin following suspension will further bolster Colombia's attacking options and Jackson Martinez, who came off the bench against Greece, expects a tougher test than in their opener.
"Ivory Coast is a team who have grown a lot, they have a lot of experience," Martinez said.
"The match against Japan was a showcase of them being a team. You have to keep controlling the game until the end."
Dider Drogba was at his influential best against Japan - helping to inspire his side's recovery from a goal down after being introduced from the bench.
Lamouchi has hinted Drogba will likely begin Thursday's game on the bench again and the 36-year-old striker is content with a bit part role.
Regardless of whether he is handed a starting berth or not, Martinez still anticipates that the Galatasaray man will be a prominent figure for his country.
"We all know his quality, he's a big forward and he's done a lot of things in his career," the Porto striker added.
"He's a leader on the pitch and can lead his team to victory when things get complicated.
"He's a key player for the Ivory Coast either starting or coming off the bench."
It will be the first meeting between the two nations and the victor can take a huge stride towards wrapping up a last-16 berth, with Japan and Greece hoping to make up ground on the losers, or on both sides if the spoils are shared.
Between them, Colombia and Ivory Coast have reached the knockout stages at the World Cup just once previously but that looks set to change ahead of what promises to be an exciting, attacking affair.
Even without the injured Radamel Falcao and Carlos Bacca, the likes of Martinez, Adrian Ramos and Teofilo Gutierrez can threaten goals for Colombia while Wilfried Bony and Gervinho will hope to add their World Cup goal tallies for the Africans.
