"We can't go too long without him," said Toronto manager John Gibbons, who described League's status as day to day.
League, 23, entered Spring Training as the projected setup man in Toronto's bullpen. Since arriving, though, he's been encountering a number of issues. Last week, League had a sore hamstring, and when he was able to get back on a mound, he caught the Blue Jays brass off guard by reverting to a lower release point.
Toronto isn't abandoning its plan to use League as its primary eighth-inning pitcher, but Gibbons admitted that the club might be forced to explore other options if League's injury persists. The Jays hope he can work off a mound again by the middle of next week.
"[If he isn't better soon], we'd have to adjust and throw somebody else into that role," Gibbons said. "We haven't talked about that yet, but we might have to in the next few days."
Right-hander Jason Frasor appears to be the top candidate behind League, who posted a 2.53 ERA in 33 games last season. Frasor has more late-inning experience than League. In 2004, Frasor led Toronto with 17 saves. Last year, he went 3-2 with a 4.32 ERA in 51 games out of the Jays' bullpen.
"You've got to like Frasor," Gibbons said. "He was our closer a few years ago."
Toronto pitching coach Brad Arnsberg had a similar sentiment last week.
"I think the job is kind of up for grabs with the experience that Frasor has," Arnsberg said. "He has a little bit more time on the mound and quite a few more big-league innings and big-league outings."
Gibbons also said that left-hander Scott Downs could be another option. Last year, Downs had a 2.77 ERA in relief, and he ranked second in the American League by holding hitters to a .134 batting average with runners on base.
Reaching higher: Toronto designated hitter Frank Thomas currently sits 13 home runs shy of 500 for his career, but he isn't focusing too much on the milestone. In fact, that total is 100 long balls shy of Thomas' ultimate goal.
"It's a great plateau -- don't get me wrong. I've got a lot of respect for it," Thomas said. "The home run number [I want to reach] is 600, so I don't even worry about 500. I want to continue to play this game for a solid four more years. You don't want to be shortsighted about things."
Thomas' 487 home runs rank 23rd in baseball history, and he is third in homers among active players, trailing only San Francisco's Barry Bonds (734) and Cincinnati's Ken Griffey Jr. (563). Currently, only four players -- Bonds, Hank Aaron, Babe Ruth, and Willie Mays -- have hit more than 600 homers in a career.
Players who have belted 500 homers have generally been considered locks for entrance into the Baseball Hall of Fame in Cooperstown, N.Y. Thomas wants to eliminate any doubt that he deserves a plaque, though.
"A goal of mine is Cooperstown. I said that 10 years ago," Thomas said. "You just can't take anything for granted, though. There's a lot of guys on that bubble that I thought would be in. Over the next four years, I really want to cement my piece of history."
Dining with the Rocket: When new Toronto pitcher Jo Matumoto -- a native of Brazil -- flew to Houston earlier this month for a tryout with an Independent League team, he didn't know he'd be running into Roger Clemens.
Matumoto said his only knowledge of Clemens came from what he saw on television, and he admitted that he was a little apprehensive to meet the future Hall of Famer.
"[Clemens] invited us to dinner on our very first night that we came," said Maria Fernanda De Luca, Matumoto's wife and translator. "It was really funny because Roger Clemens, for us, we have the impression of him being really tough. He's a sweetheart.
"I always saw him on TV and I thought he was the mad type -- intense. He's not, he smiles a lot and he's a nice person. He said, 'Good luck. Anything you need, I'm going to help in any way I can.'"
Injury update: Left-handed reliever Davis Romero continued to be hampered by a shoulder injury, and he sat out of activities on Friday. Right-hander Francisco Rosario's lower back was feeling better, and he was able to throw off a mound.
Quotable: "It's the sort of thing that kind of captures your heart. No one could catch him. His training regimen consisted of throwing a ball against a wall." -- Agent Randy Hendricks, talking about the 36-year-old Matumoto, who signed a Minor League contract with the Jays on Friday
Jordan Bastian is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.