The 24-year-old, who can play at left-back or centre-half, featured for the Cobblers in a behind-closed-doors practice match at Stoke on Tuesday afternoon.
Boss Aidy Boothroyd told the media ahead of his side's home fixture against Rochdale on Saturday: "We had a look at Lee the other day and I like him.
"If you're going to be successful and get out of the division at the right end then you've got to get players in who are better than the level you are at.
"Lee certainly is that and we'll be looking at doing something with him in the next couple of days."
