The teams have discussed Street, but their talks have yet to include Kennedy, sources say. In addition, a package deal might be difficult to complete with the Padres controlling both Street and Kennedy through 2015.
The Padres likely will trade their potential free agents, third baseman Chase Headley and outfielder Chris Denorfia. They are taking offers for both Street and setup man Joaquin Benoit. But they are "lukewarm" on moving Kennedy, sources say.
Street, named to the National League All-Star team on Sunday, would give the Angels a potentially dominant bullpen, enabling them to move right-hander Joe Smith back to a setup role.
Kennedy would fortify a rotation that includes several pitchers with scant major-league experience and currently is without left-hander C.J. Wilson, who went on the disabled list Thursday with a sprained right ankle.
The Angels' farm system ranked last in the majors in Baseball America's most recent talent rankings. For general manager Jerry Dipoto to land both Street and Kennedy, he might need to trade pieces off the team's major league roster.
Dipoto already has made two additions to his bullpen, left-hander Joe Thatcher and righty Jason Grilli. Triple-A second baseman Taylor Lindsey, the Angels' top prospect according to BA, likely would be one Padres target. The Angels also are deep in young relievers who could supplement any trade.
The Padres, meanwhile, are in the middle of a front-office transition. They fired general manager Josh Byrnes on June 23, and assistant GM A.J. Hinch currently is the point man in trade talks, with input from club executives Omar Minaya and Fred Uhlman Jr.
The bigger obstacle to deals, rival clubs say, is that Padres ownership might not be eager to part with talent because of its desire to rebuild quickly. The Pads entered the All-Star break with a 41-54 record, leaving them in third place in the National League West, 12 games behind.
Ownership signed one trade candidate, outfielder Seth Smith, to a two-year, $13 million extension shortly after firing Byrnes. The team holds a $7 million option on Street and could bring Kennedy back in his final year of arbitration for $9 million to $10 million. In addition, the Padres could make Kennedy a qualifying offer after the 2015 season, ensuring that they would receive a high draft pick if he departed.
Street, one of the top closers on the trade market, is 24-for-25 opportunities this season with a 1.09 ERA. Kennedy has a 3.47 ERA in 20 starts, with 133 strikeouts and 34 walks in 124-1/3 innings.