McAllister is currently on the 15-day disabled list due to a lower back injury.
"We have some things to think about moving forward," Francona said. "We tried to explain to Zach that, 'Hey, go do your thing, because we're juggling multiple things, but not to worry about that. Go concentrate on pitching like you can pitch and let us take care of those other things.'"
Francona said the team felt House, who has posted a 5.24 ERA in 22 1/3 innings this season, deserved another start. The manager was also quick to note that the Indians have a pair of off-days (June 23 and June 26) on either side of a two-game Interleague road series against the D-backs. Cleveland will need to shuffle its rotation that week to keep other starters from having too many days off between outings.
On the season, McAllister is 3-4 with a 5.89 ERA through 10 starts. After opening this season 3-0 with a 2.28 ERA through four starts, during which he held opponents to a .655 OPS in 23 2/3 innings, McAllister went 0-4 with a 9.51 ERA in the six starts (.919 opponents' OPS in 23 2/3 innings) leading up to the DL stint.
In a Minor League rehab outing with Columbus on Tuesday, McAllister allowed two runs (each on a solo home run) on three hits in six innings. The big right-hander struck out six and walked two in the outing.
"I was really happy with it," McAllister said. "I put my fastball where I wanted to, pitched down in the zone and was able to get a lot of soft contact and some broken bats. That's the main thing any time you're pitching, to pitch down in the zone and put the ball where you need to."
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.