Suazo suffered a small tear in his left hamstring in a friendly match against Israel on May 31 and was ruled out for two to three weeks.
But he has been in light training at Chile's World Cup base near the town of Nelspruit and might be back in action in time for the Group H match on June 16.
"He started running again yesterday. He's a very important player for us so we're all happy to see him training again," Chilean captain and goalkeeper Claudio Bravo told reporters.
Mark Gonzalez, who is hoping to partner Suazo in attack, described his team mate's fitness as "delicate" and said: "We all hope that Humberto can play in every match.
"But we have to be realistic and it might be better if he misses one or two matches and is 100 percent fit for the third."
Suazo was one of the main reasons that Chile qualified for the World Cup. He beat the likes of Uruguay's Diego Forlan and Brazil's Luis Fabiano to finish as top scorer in the South American qualifiers with 10 goals in 18 games.
But he injured his shoulder in April while playing for Spanish side Real Zaragoza and has hardly played since.
