Altidore has played just 23 minutes of his country's FIFA World Cup campaign after sustaining what looked to be a serious hamstring injury in the USA's 2-1 win over Ghana on June 16.
But the Sunderland striker has responded well to treatment and was jogging at the team's training session in Sao Paulo on Friday without any difficulty.
"We are very optimistic (of Jozy's fitness)," Klinsmann said.
"Every day is a big step forward. Eleven days now and he's looking better every day."
Altidore is a key cog in the US setup, with his pace and strength as a target-man regularly bringing others into play.
In his absence, captain Clint Dempsey has been shifted into the role of lone striker, somewhat diluting his impact on games.
And Klinsmann acknowledged that Dempsey – if he plays on his own up front - needs far more support if the US are to pull off a last 16 surprise against Belgium.
"We have to bring the players higher up, get more support for Clint. Something we'll work on next few days," he added.
