"We still have one training session which will take place in a short while," Bielsa told a news conference at the Mbombela Stadium where their opening Group H match will be played.
"I haven't yet decided on my starting lineup. Suazo has been coming along over the last few days and he's been training in the same way as his team mates.
"Nevertheless, physically, he's still feeling the effect of the rest he's had to take ever since the Sunday on which he injured himself," he added.
Suazo suffered a hamstring injury in Chile's 3-0 win over Israel on May 30 and has not played since. That match marked his comeback from a month-long lay off with a shoulder injury.
"He has been able to train over the past three days and he has been able to train fully, 100 percent," Bielsa said.
"Now, if you're asking me is he back in the same shape as he was before his injury, then he's not in the same shape. But if you're asking me if he's healthy, yes he is healthy in the sense that he can take on the same tasks as the other players."
Suazo was top scorer in the South American qualifying campaign, with 10 goals in 18 matches.
If he fails to start, his most likely replacement would be Esteban Paredes, who looked sharp in the 2-0 defeat of New Zealand in a warm-up match last week.
With Chile favourites to beat injury-plagued Honduras, Bielsa might be tempted to start with Paredes and bring on Suazo only in an emergency.
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