Reports originally stated that the England international could be sidelined for 10 weeks after suffering an ankle injury during Liverpool's 1-0 win over Manchester United on September 1.
Despite the initial injury layoff, it has emerged that a six-week spell on the sidelines is a more realistic term for the full-back.
Johnson appears to have confirmed these reports by writing on Twitter: "Injury doesn't seem as bad as first thought, hopefully be back sooner than originally expected! #BetterNews."
Meanwhile, striker Daniel Sturridge is expected to be fit for Liverpool's Premier League match against Swansea City on Monday following a thigh problem.