The Wales captain has been strongly linked with a move away from the Liberty Stadium this summer having led his side to League Cup success last season, though Swans chairman Huw Jenkins has previously confirmed the he has had no approaches from any club.
Liverpool and Everton have also been linked with the 28 year old, who is valued at around £10 million.
However, Williams has insisted that he is focussed on the task at hand, despite holding ambitions of playing in the Champions League.
Arsenal are expected to attempt to wrap up a number of deals before the transfer window closes on September 2nd having so far failed to land any of their top transfer targets.
Williams played the full ninety minutes of Swansea’s opening day 4-1 defeat to Manchester United.