UPDATE: Peterson tweeted late Tuesday night he signed a five-year contract extension with the Cardinals worth up to $70 million.
Getlin said there are "still hurdles to clear" before a contract is signed, but there's a "good chance" it gets done shortly.
Peterson has been named to the Pro Bowl in each of his first three NFL seasons, as a kick returner in 2011, and as a cornerback in 2012 and 2013. He still has two years remaining on his rookie contract but has been negotiating with Arizona about a possible extension.
On Monday, Cardinals coach Bruce Arians said that Peterson will be concentrating solely on the defensive side of the ball this season, and will see limited punt-returning duties.
In 2011, Peterson set the record for the most punt return yards by a rookie in one season.
Peterson grabbed three interceptions and made 42 tackles in 2013.
- Molly Geary and Will Green