Longoria, out since May 1 with a partially torn left hamstring, ran the bases about a dozen times at a near-game speed before the Rays' game Saturday night against the Miami Marlins, according to the newspaper.
Afterward, the All-Star said he hopes to return to the Tampa Bay lineup after just a few rehab appearances, but he also admitted the final decision is up to manager Joe Maddon and the team's training staff.
"It's a struggle between me and them sometimes," Longoria told the Tribune. "And I understand that their job is to be cautious and get me back to stay for the whole year, but that's definitely my goal, too.
"We've been going back and forth as far as when I'm going to come back and play, and I think the goal now is we're going to go back home, run the bases again on Tuesday, and if that is all fine and good, hopefully, I'll go out [on the rehab assignment] after that."
Maddon said he won't push Longoria.
"We're interested in playing the last game of the season this year and winning it, and we're not going to do it without him, so it's really important that we be patient and follow the practices that permit him to be there when we need him most," Maddon told the Tribune.
Longoria was hitting .329 with four home runs and 19 RBIs before suffering the injury.