The People says Wenger spoke with Williams after Arsenal's victory over the Swans last month.
Wenger is understood to have personally congratulated Swansea captain Williams on a wonderful season.
And over the past fortnight Wenger is believed to have made it clear he is interested in signing £9million-rated Williams.
Liverpool boss Brendan Rodgers has been confident his relationship with Williams will help the Reds win the race to sign the 28-year-old in the summer.
But Wenger has seemingly attempted to add his own personal touch in a bid to make Williams think twice about snubbing the Emirates in favour of the club he supported as a boy.