The 27-year-old faced a four-month lay-off if he needed surgery, but a scan has shown the ligament is healing.
"The next big moment is in four weeks when it's scanned and hopefully shows more repair," coach Tony Smith said.
"It's not a four or five-week injury. It's an eight, nine, 10-week injury if it goes well, and so far it is."
The former Parramatta scrum-half won the Super League Player of the Month awards for February and March and was described by Smith as "world class" prior to picking up the injury.
England back Stefan Ratchford has stepped into Sandow's role but league leaders Warrington have lost their last two matches, against St Helens and struggling Huddersfield.
Smith added: "You miss somebody special like that. He was red hot, the stand-out player in Super League, but you've got to make do. You've got to get the next lot doing the job.
"The last couple of weeks have been a kick up the backside for us in some areas. We need not just one or two, but people across the board, to pick it up."
Warrington will be without half-back Chris Sandow for two months as he recovers from a hamstring injury picked up in their win at Wigan on 1 April.