The former Manchester United man sustained the damage in the 2-0 defeat at West Brom on September 1, with the original prognosis predicting a two- or three-week absence.
Gibson's hint at a swift return to action is positive news for the Toffees, who have struggled in his absence, dropping seven points in the Premier League.
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David Moyes' men followed the defeat at the Hawthorns with a draw against Newcastle and whilst they went on to beat Swansea and Southampton, they were held by Wigan last time out.
However, Gibson could well be close to a return after posting on his Twitter account: "Scan went well 2day #buzzin :)”
Everton resume their league campaign away at Loftus Road on Sunday, although this fixture may come too soon for Gibson, who will be targeting a return in the Merseyside derby against Liverpool on October 28.