After suffering a torn meniscus in his right knee, Floyd was placed on the 15-day disabled list on April 9. He has since undergone successful surgery and has recently been taking at-bats in Florida during extended Spring Training.
On Tuesday, Maddon said that Floyd had four at-bats and reported no pain. The manager was also happy with Floyd's progress.
"He felt pretty good overall," Maddon said of Floyd. "He wasn't pressed on the running side of things, but he ran well. Nothing went wrong. He had a pretty good day today."
With Floyd progressing well, Maddon said it was a possibility that the designated hitter would be back with the team in time to play at home against the Angels this weekend, or the Yankees early next week.
"I just want him back whenever he's ready to come back," Maddon said. "We've got the Yankees for four games coming up and there is also pinch-hitting possibilities playing in the [upcoming] National League games. He has NL experience."
Tampa Bay signed Floyd as a free agent in the offseason. Before he got hurt, the 35-year-old was hitting .333 (5-for-15) with two home runs and five RBIs in four games this season.
David Singh is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.