Ken Rosenthal of The Athletic reported the Angels' interest, but he added that Cozart is also in discussions with other teams as he pursues a deal.
The Angels have been one of the most active clubs in MLB this offseason, starting with the surprise signing of Japanese star Shohei Ohtani last week. They acquired Ian Kinsler in a trade with the Detroit Tigers on Wednesday.
Cozart doesn't seem like an immediate fit for the Angels, who have Andrelton Simmons locked in at shortstop.
Given Simmons' value on defense, where he has won three Gold Gloves and led MLB with 32 defensive runs saved last season, Cozart would likely have to switch positions.
Third base is a position the Angels need to upgrade after getting a collective .238/.318/.395 slash line from the position in 2017.
The 32-year-old Cozart is coming off the best year of his career last season. He hit .297/.385/.548 with 24 home runs in 122 games.