We probably won’t take a look but he would be an instant upgrade and two years younger than Richard Sherman coming in.
I think Sherman's more recent play at corner is better (2019, not 2020 when he was fighting injury). Sherman has never really relied on speed, while Peterson has. Speed tends to fall off over the years.
PFF, for whatever you might think of it it, had this to say about Sherman in November 2019:
1. Richard Sherman, San Francisco 49ers
As PFF’s highest-graded cornerback, Richard Sherman has regained his dominance by perfecting a top-down technique that allows him to use his 6-foot-3 frame in the 49ers' single-high man-to-man or deep Cover-3 zone scheme. Sherman has always been a smart and savvy player who is a perfect fit for press coverage with a mix of both man and zone coverage. He has the NFL’s 10th-best forced incompletion rate (17.6%) and has allowed only one touchdown across 517 coverage snaps.
Above all, Sherman has the most coveted trait you want in any pass defender — he doesn’t allow big pass plays downfield. In 2019, he allowed only 8.4 yards per reception, third-best in the league, while just 13 of his 51 targets were converted to a first down, which was the fourth-best total by any player at his position.
Sherman plays with plenty of swagger, but his performance is backed up with plenty of substance, as evidenced by the fact that opposing quarterbacks have managed a passer rating of just 46.8 when throwing his way. As he wraps up his ninth NFL season, Sherman has hit the sweet spot of consistency by bringing his A-game to a top-10 defense.
At that same point, Peterson wasn't even ranked in the top 25 for the year.
Then after the season, it had this:
2. Richard Sherman, San Francisco 49ers
A torn Achilles threatened to torpedo Richard Sherman’s career, but last season
he showed how good he could be when he is at his best and 100% healthy. Though he had a rough Super Bowl, Sherman allowed just 373 yards and one touchdown all season long, including the playoffs. Passes thrown his way resulted in a passer rating of only 45.3, or barely better than if the quarterback had just thrown the ball away every play instead. Sherman’s physical tools may be on the wane as he gets older, but he may be the smartest cornerback in the game and has a freakish understanding of how an offense tries to attack him.
13. Patrick Peterson, Arizona Cardinals
At this point, there’s significant doubt as to what the real Patrick Peterson actually is. Between suspension, illness and fluctuating performances, Peterson has been all over the map in terms of PFF grades but has always been some variety of good. Last year marked some of the worst numbers of his career, being beaten for a passer rating of over 100 for the first time in a season (104.6), and with him now over 30, it’s fair to wonder if he will return to his very best play. If he can, Peterson will jump up this list in a year’s time, and he is only a year removed from a PFF coverage grade of 83.7.
I can't find any final rankings for after the 2020 season, so someone can feel free to add them. At this point, I'm interested in Peterson, but more as a free safety prospect if the price were right. He would give us the type of player who could even switch to corner in nickel situations or cover tight ends.