The Australian midfielder picked up a foot injury during the pre-season friendly with Werder Bremen on Tuesday.
There were fears that Cahill could be sidelined for three months with the problem, but such a scenario has been played down.
However, the former Millwall man, who broke a metatarsal last season, will sit out the opening weeks of the campaign.
"It is premature to suggest three months out, that is wide of the mark," head physio Mick Rathbone told the club's official website.
"He has damage to the same area of the foot as last time, but it is minuscule in comparison to the previous injury."