Longoria took "20 or so" swings on Sunday morning off of hitting coach Derek Shelton.
"It went as good as it could go, no pain," Longoria told Topkin. "Huge step forward today."
Longoria will go to Minnesota with the team this week and hopes to take full batting practice on Wednesday and Thursday before going on a rehab assignment.
The Rays could get him back sometime during a six-game homestand from April 29-May 5. The Rays host the Angels for three games, have an off day on Monday, May 2, and then play three more against the Blue Jays.
Longoria would like to play just two or three games with Double-A Montgomery, while the Rays may prefer him to play five games or so, Topkin writes.
"I know I didn't spend that much time in the minor leagues," Longoria said, "but I don't want to go back and spend any more."For more baseball news, rumors and analysis, follow @cbssportsmlb on Twitter or subscribe to the RSS feed.