The Gunners are understood to be keen to take the Wales international to the Emirates this summer, as Arsene Wenger looks to strengthen his defensive options.
Wenger is understood to have enquired about Williams during the January transfer window, only to be told that the Swans didn't want to sell the 28-year-old.
Recent reports have suggested that Arsenal have now made a firm bid to sign the former Stockport man, but Jenkins has been keen to point out that no contact has been made between the two clubs.
The French boss has reinforced the idea that he is prepared to spend money during the summer, amid some unrest from fans who would like to see the club pushed forward to challenge for titles.
Arsenal last week