Ramirez, 39, has been working out in Miami since December and has plans to have open workout sessions for clubs interested in his services at the end of January.
"The Orioles and Blue Jays saw Manny work and Baltimore liked what it saw, but Oakland has been the team that has expressed the most interest, even before having him work out," the source said.
Ramirez, a .312 lifetime hitter with 555 home runs and 1,831 career RBIs over 19 seasons, was reinstated by Major League Baseball from the "voluntarily retired" list after the Dominican player opted to leave the game instead of serving a second suspension for violating the league's banned substances policy in 2011 while playing for the Tampa Bay Rays.
In an agreement reached with MLB, Ramirez must serve a 50-game suspension upon finding a team that will sign him instead of the customary 100-game suspension levied on repeat offenders.
"Every day that goes by I regret the decisions I made due to bad advice," Ramirez told ESPNDeportesLosAngeles.com in December. "We're all human and we make mistakes. Everyone deserves an opportunity to show that they have changed."
Enrique Rojas is a reporter and columnist for ESPNdeportesLosAngeles.com and ESPN.com.