The right-back was initially expected to be out for 11 weeks after suffering damage to his ankle in the 1-0 win over Manchester United, but is now positive over a quicker recovery
The right-back was forced off with 11 minutes to play as the Reds beat rivals Manchester United on September 1, and was pictured leaving Anfield on crutches.
Johnson was forced out of contention for England World Cup qualifying double-header against Moldova and Ukraine, with an 11-week layoff initially predicted, but he has now revealed he hopes to return sooner.
"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 the only team to maintain a 100 per cent record following the opening three rounds of Premier League fixtures, and travel to Swansea City on Monday.