Williams told BBC Radio Cambridgeshire: "I've never fallen out with anybody here and I love the club; I've been back here four times."
"If I was offered something that was suitable, I would definitely sign."
He added: "I'm keeping my options open because I've got one little boy who's about to start school and another child on the way."
Williams made his first Posh appearance since returning from his loan spell against Tottenham in the FA Cup third round this month. It was also his first match under new boss Mark Cooper.
Meanwhile, Danny Andrew has joined Cheltenham Town on a month's loan, and Southend have confirmed that Posh were the Championship club who failed to agree terms with their right-back Simon Francis.
"I listened to what Peterborough had to say, but it didn't seem right at the moment," Francis told the Southend website.