Britton is yet to make a competitive appearance this term after sustaining severe bruising on his knee during pre-season.
But a statement on Swansea's website on Thursday said of the 32-year-old: "His recovery stepped up a gear this week as he is now going through running drills with a view of returning to first-team training soon."
Apart from half a season spent at Sheffield United, Britton has been with the Swans since 2002, having initially been on loan.
Source : PA
Source: PA