The A's will make the announcement on Friday, the Chronicle reported.
Conversations between Garciaparra, who had been contemplating retirement, and the A's have been percolating for a couple of weeks.
Garciaparra, 35, batted .264 in 55 games for the Dodgers last season, as he battled injuries. Oakland's interest in him is presumably to help the A's balance their lineup: The right-handed-hitting Garciaparra hammered lefties last season, going 19-for-56, with four homers and a 1.067 OPS.
A six-time All-Star, Garciaparra started his career with the Boston Red Sox, hitting 30 or more home runs twice and driving in 100 or more runs four times in nine seasons. He was the AL Rookie of the Year in 1997 and was second in the AL MVP voting in 1998.
Information from ESPN The Magazine senior writer Buster Olney and The Associated Press contributed to this report.