Allen, on the injured list for a time with a sore left elbow, is 0-2 with an 11.72 ERA in five starts for the Clippers.
“One way or the other, we have to come up with a starter on Sunday or Monday,” said Francona.
The Indians selected the contract of right-hander Justin Garza from Columbus to take Civale’s spot on the roster.
“Garza was actually pitching in kind of long relief in Triple-A and really doing a good job,” said Francona.
Civale suffered the injury throwing his last two pitches Monday with two out in the fifth.
“The one thing I know with this injury is you’ve got to get rid of it before you start letting him throw or it can lead to other issues,” said Francona.
Hedges was hit in the head by a pitch on June 11 by Seattle’s Justin Dunn.
Hedges, who drove in a second-inning run Thursday night, said he started feeling better about three days ago.
If all goes well, the next step would be to throw batting practice or a simulated game before going on rehab.
Rosario spent six years with Minnesota before signing with the Indians as a free agent over the winter.
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