The Gunners attempted to sign the Welshman back in January, but have now reignited their interest as they prepare for the upcoming season.
According to Daily Mail, Arsenal are on the verge of reaching an agreement with the player, although they have yet to persuade Swansea to sell.
For the time being, the Swans are not interested in doing business with Arsenal, but they are unlikely to stand in the player’s way if he expresses his desire to join the Gunners.
Ashley Williams, who joined Swansea when the club were in League One, has proved his worth in the English Premier League, missing a total of two games over the last two campaigns.
He has established himself as one of the best central defenders in the elite division and it appears a big club move is on the cards.