The right-back was hurt in a collision with Patrice Evra during Liverpool's Premier League victory over Manchester United last month and left Anfield on crutches.
The injury ruled him out of England's World Cup qualifiers against Moldova and Ukraine, and reports this week suggested he could be out for 10 weeks.
But, writing on his Twitter page on Thursday, Johnson gave an upbeat bulletin on his fitness.
"Injury doesn't seem as bad as first thought," he wrote. "Hopefully be back sooner than originally expected! Thank you everyone for the 'get well' messages!!!"
Liverpool are yet to give a likely date for Johnson's return, but Brendan Rodgers could have Daniel Sturridge fit for Monday's trip to Swansea.
Sturridge's ongoing groin problem stopped him joining up with England, but he is expected to be part of the squad which travels to Wales.
The striker has scored three winning goals in three Premier League games this season to leave Liverpool top of the table.
Swansea v Liverpool is live on Monday Night Football on Sky Sports 1HD at 7pm