NFL source: Rafael Bush hoping for shot at starting role with Falcons

Safety Rafael Bush says he has enjoyed his two seasons with the Saints, and he especially liked playing under defensive coordinator Rob Ryan in 2013.

But after he hit restricted free agency this offseason, the Atlanta Falcons offered him a two-year deal worth up to $4.5 million to play for them instead, a league source said Friday.

Bush signed the offer sheet. The Saints can keep him if they match the Falcons’ offer sheet by Tuesday. But Bush would prefer it if New Orleans let him move on, the source said.

It’s nothing personal against the Saints, who in March extended Bush a one-year, $1.4 million tender that ensured they would have the chance to match any offer sheet the safety signed, the source said.

According to the source, in Atlanta, Bush is being offered a chance to be a starting safety alongside William Moore, a friend. The Falcons’ release in February of safety Thomas DeCoud, a starter since 2009, created the opportunity.

In New Orleans, the safeties who are expected to see the most action are Jairus Byrd, who was acquired in March in free agency and whose 22 career interceptions are the most among players at his position since he entered the league in 2009; and Kenny Vaccaro, a 2013 first-round pick who had an excellent rookie season.

“Atlanta is a better situation for Rafael Bush to have a starting role in the defense,” the source said. “It is a better situation for his career and for his family,” especially financially.

Last year, Bush was credited by the Saints with 45 tackles (29 solo), six pass break-ups, a forced fumble and a fumble recovery over 13 games and six starts.

He also tacked on four special-teams stops as the Saints — whose defense was ranked No. 4 overall and second against the pass — won 12 of their 18 games and made it to the divisional round of the NFC playoffs.

Bush handled an increased workload well early in the season when safeties Malcolm Jenkins and Roman Harper (neither of whom are on the team anymore) were injured. The analytics website Pro Football Focus gave Bush the 24th-highest grade among NFL safeties in 2013 and rated him as the Saints’ best player at the position.

Bush’s career began in Atlanta as an undrafted free agent in 2010, and he was on the Falcons practice squad until Denver signed him away in 2011. He played sparingly for the Broncos, who waived him at the end of August 2012. New Orleans soon claimed him.

Bush, who played at South Carolina State, played in all 16 games for the Saints in 2012 and led the special teams with 15 tackles and a fumble recovery. His role on defense initially grew after Jenkins suffered a hamstring injury and landed on injured reserve: He had an interception, which he returned 40 yards; forced a fumble; and recovered another fumble.

The Saints haven’t said whether they intend to match Bush’s offer from Atlanta.

For now, the only other Saints safety aside from Vaccaro and Byrd is Marcus Ball, signed from the Canadian Football League earlier this week. The Saints on Friday also reached terms with 12-time Pro Bowl defensive back Champ Bailey, who had been a free agent since Denver released him in March.

It has been speculated that Bailey, who turns 36 in June, could play as a cornerback-safety hybrid.