Cordero has allowed an earned run in four of his past five outings, losing one game and blowing two saves over that stretch.
The veteran was supposed to be a security blanket for the Blue Jays in the event anything happened to Santos, but he's off to a shaky start this season. The struggles, however, haven't discouraged manager John Farrell.
"He gives you everything he has," Farrell said. "He's going to force the opposition to beat him, he doesn't create issues for himself by an abnormal number of walks. He has tremendous experience and success in the role.
"He's our closer."
Cordero has converted just two of his four save opportunities and carried a 5.73 ERA into Wednesday's series finale against the Rangers.
After Toronto's bullpen tied the Angels for most blown saves in 2011 with 25, the club traded for Santos, who saved 30 games with the White Sox, and Cordero, who had 37 with the Reds last year, in order to revamp one of its greatest weaknesses. However, the bullpen has been a disappointment thus far, as the Blue Jays have blown six saves -- tying them with the Angels for the most in baseball -- and have a 4.52 ERA, which is the fourth-worst mark in the American League.
Cordero, 36, is second on the active saves list with 329, trailing Yankees closer Mariano Rivera.