The contract reportedly is worth $15.3 million with $6.8 million guaranteed.
It appears that Hayward will replace Patrick Robinson, who is an unrestricted free agent.
Hayward split time between the slot position and an outside cornerback spot and led all Green Bay Packers cornerbacks in playing time last season. He was on the field for 88.1 percent of the defensive snaps.
However, Hayward failed to record an interception after picking off nine passes in his first three seasons combined, including six as a rookie in 2012.
Robinson had a bounce-back year in 2015 in his first season with the Chargers, totaling 49 tackles, eight pass breakups, an interception and a forced fumble in 16 games. Robinson was used mostly as a slot defender, but also made 10 starts because of injuries to Brandon Flowers and Jason Verrett.
Robinson played in 661 defensive snaps and was the only defensive back to play in every game for the Chargers.
A first-round selection in the 2010 draft for the New Orleans Saints, Robinson turns 29 in September. He has 10 career interceptions and 54 pass breakups.
ESPN Packers reporter Rob Demovsky contributed to this report.