Hill is on the 15-day disabled list with a hamstring strain. He will take live batting practice on Wednesday before appearing in an extended Spring Training game later in the day.
The 29-year-old is then expected to appear in three games for Class A Dunedin. If everything goes well, Hill's plan would be to return to Toronto on Sunday, with the opportunity to be activated in time for the game the following day against Detroit.
Hill was originally planning to be back Thursday, but the organization convinced him to be a little more patient with the injury.
"I was hoping to, but it's probably better," Hill said. "I feel great right now, but another two, three days -- especially the at-bats -- are going to be big just to get the timing down.
"They want to see me go through a full game for a couple days, and they're comfortable with the schedule we kind of lined out for the next few days. If nothing happens, I'll be back Sunday."
Hill suffered the injury while attempting a stolen base against the Yankees on April 19. The native of California already has six stolen bases on the season, which matches his career high from 2009.
He joked on Tuesday that he'd like to get another stolen base out of the way to prove he can handle it.
Toronto's manager isn't quite so sure. John Farrell said it's possible the club would take a cautious approach with the former Silver Slugger Award winner once he gets back to full strength.
"I think we have to be smart about it," Farrell said. "Obviously now there's a pretty clear history of some quad and hamstring issues, and we've got to factor that in."
Hill was hitting .242 with nine RBIs and four runs scored before getting placed on the DL.