Ferguson stated on Tuesday night, in the aftermath of United's Champions League win over Roma, that Hargreaves would be missing for at least four weeks, ruling him out of England's Euro 2008 double-header with Estonia and Russia, plus a series of key club games, including the trip to Dynamo Kiev on October 23.
However, the Red Devils chief now feels Hargreaves' return could be slightly more speedy.
"It may be a bit less than four weeks," Ferguson told Manchester United Radio.
"Owen should be back training in about 10 days' time, which is good news because he hasn't had the best of luck.
"But, having the injection has been successful."