Rodriguez, the top scorer in Brazil 2014 with six goals in five matches, missed a training session in Kazan on Friday due to muscle fatigue. His left calf has reportedly been troubling him.
The 26-year-old trained at the Mordovia Arena in Saransk on Monday but his state of fitness was still unclear.
"We are waiting to see what the doctors will say after the last check," Colombia coach Jose Pekerman told a news conference.
Great expectations have been placed on Rodriguez as the spearhead of the best generation of Colombian players since the 1990s. He won over many neutral fans in Brazil for his spectacular style -- and his salsa-dance goal celebrations.
But his club performances since 2014 have been inconsistent and he is currently on loan to Bayern Munich from Real Madrid.
Pekerman insisted several other players could step up to the mark should Rodriguez not take the field on Tuesday.
"We always wait until the very last minute before we decide," Pekerman said.
"World Cups are played after a very heavy season. It is true some players arrived here in Russia not feeling very comfortable. They have all improved very much, even if some of them are a little tired."
One ace up his sleeve is striker Radamel Falcao, Colombia's all-time top scorer. "El Tigre" is raring to make his World Cup debut, having missed the 2014 tournament through injury.
Pekerman mentioned Jose Izquierdo, Juan Quintero and Mateus Uribe as potential matchwinners.
"We have enough players for all alternatives," he said. "Our team is much richer, much stronger (than in 2014). We've got much more flexibility."
If Rodriguez's absence would disappoint Colombia's legions of fans, it would be a relief to Japan coach Akira Nishino.
Colombia walloped Japan 4-1 in the group stage in 2014 on their way to the quarter-finals, with Rodriguez among the scorers.
"He is almost like a symbol of the Colombia team, a points-getter, a mood-maker," Nishino said. "It is difficult to mark him. Who is going to mark him? The whole of the team. We cannot give him time or room.... he is everywhere on the pitch."
With Colombia ranked 16th by FIFA and Japan 61st, "Los Cafateros" (the Coffee-makers) are favoured to win. But Pekerman made clear he was not under-estimating the Blue Samurai and their quick, fast-breaking style.
Group H, which also features Poland and Senegal, is one of the more open of the tournament.
"We think Japan is going to be a very tough team. We have completely forgotten what happened in the last World Cup," said Pekerman, an Argentine who has managed Colombia since 2012.
"In the short term our main aim is to go through to the next stage. The group phase is really tough. We'll see what happens this time. We hope to be at least as good or better than four years ago."
(Reporting by Angus MacSwan; Editing by Ed Osmond)
