Both have made compelling cases for a spot in the rotation, a competition that includes Tyler Duffey, Jose Berrios, non-roster invitee Ryan Vogelsong and Rule 5 Draft pick Justin Haley. After frontrunner Trevor May went down with a season-ending ulnar collateral ligament tear -- and Berrios is with Team Puerto Rico in the World Baseball Classic -- both are getting an extended look this spring.
"We are all watching as guys get further along, throwing more pitches and more innings against better competition," Twins manager Paul Molitor said.
Mejia, who got the start on Wednesday, picked up the win after he threw 3 2/3 scoreless innings, scattering four hits while striking out eight and walking none. He has not allowed an earned run since his spring debut against the Boston Red Sox on Feb. 25 -- a span of four outings.
"I'm just going out there trying to do my job and whatever they ask me to do," Mejia said through a translator. "I always want to do something to help the team. That's always the goal, to be on the big club and help the team win."
The Dominican native was brought in as part of last season's Trade Deadline deal that sent Eduardo Nunez to the San Francisco Giants. At age 23, Mejia still has plenty of potential but that means he also has Minor League options. Molitor has been impressed with Mejia so far this spring, so even if he doesn't break camp with the big league team, there is a good chance that he could be the first name called up from Triple-A Rochester if the need arises.
"He's getting a chance to get extended and I think he realizes that we are trying to take a good look at him to see where he's at," Molitor said. "He's a different pitcher than the brief look we got of him last year in terms of what he can do with a baseball."
Tepesch is on the other side of the spectrum. Signed as a Minor League free agent with an invitation to Major League camp this offseason, Tepesch is trying to re-establish himself at the big league level after missing significant time over the last three seasons due to injuries. After winning a job in the Texas Rangers' rotation in 2014, Tepesch began feeling discomfort in his throwing elbow that limited him to just 23 games.
While rehabbing, he was diagnosed with thoracic outlet syndrome that required the removal of a rib, similar to the procedure fellow Twins starter Phil Hughes went through last season. Tepesch missed the entire 2015 season and made just one big league start in 2016, while spending time with the Rangers, Athletics, Royals and Dodgers organizations.
Tepesch hasn't allowed an earned run in his last three outings and has held opponents to a .192 average this spring.
"All I can do is take the ball every time I get it and try to put up zeros," Tepesch said. "I can't really worry about doing anything other than that."
If Tepesch, who has an opt-out clause in his contract, is unable to crack the rotation to start the season, the 28-year-old said he is open to a role in the bullpen.
"Wherever I can fit in, whatever they want me to do, it doesn't really matter to me as long as I'm able to help this team," Tepesch said. "I'm just looking for an opportunity to continue to go out there and compete."