Free agent cornerback Tramon Williams is back home thinking after his visit with the New Orleans Saints, according to a league source. But the Saints remain in play for his services.

It’s unclear if the Saints made an offer to the longtime Green Bay Packers standout or if other teams are competing to sign him.

Meanwhile, the NFL Network’s Ian Rapoport reported that the Saints made a “major push” to sign former New England Patriots cornerback Brandon Browner, offering more than $5 million per year.

The Saints have made the cornerback a top priority this offseason – as coach Sean Payton said they would last month. Here’s what I wrote about Williams and what I wrote about Browner when the Saints lined up visits with them on the opening day of free agency. It’s unknown if New Orleans would sign both top corners or if it’s an either-or proposition.

The Saints have room to add more than one top corner. Last year, Patrick Robinson, Corey White, Terrence Frederick, Brian Dixon and Stanley Jean-Baptiste rotated into the No. 2-4 cornerback spots with erratic results. Robinson is an unsigned free agent himself.

Keenan Lewis is the Saints’ No. 1 cornerback – though he threatened to hold out of OTAs and minicamp if the Saints won’t guarantee the remaining three years of his contract. That’s an unfortunate development for New Orleans since Lewis was arguably the most valuable player on the defense last year.

It seems unlikely that the team will cave to Lewis’ demands. But it also seems unlikely that New Orleans will let Lewis go, since the $13 million they owe him over the next three years is a substantial bargain compared to the deals being signed by similarly-rated cornerbacks in free agency this year.