Such an alignment would be employed for several reasons, manager Ozzie Guillen outlined before the Sox's 7-5 victory Saturday night at Detroit.
Floyd could get an extended look as a starter if he pitches well in place of the struggling Jose Contreras, who spent Saturday night in the bullpen with the Sox relievers.
Floyd is a candidate to start next year, but he was tagged for 11 hits in 4 2/3 innings in a start against the Tigers on July 24 and has surrendered eight home runs in his last 14 1/3 innings.
Another consideration would be to preserve the left arm of John Danks, who has pitched 112 innings in his first major-league season. Danks threw a career-high 156 innings in the Texas organization in 2005 and 140 last season.
"One inning at the big-league level is two innings in Triple-A, mentally and physically," Guillen said.
The last reason would be to give Contreras a shot at resurrecting his season, which could lead the Sox to keeping him or helping him increase his market value in trade.
Guillen believed that skipping a turn would help Contreras (5-14) mentally as well as physically. Contreras has lost seven consecutive decisions and hasn't won a game since June 18.
Thursday, Contreras said he would rather be traded if he doesn't start for the Sox next season.
He will be paid $10 million in each of the next two seasons, making it tough for the Sox to move him unless he can raise his stock.
"I don't know exactly if we're going to do that, but we might," Guillen said of a six-man rotation. "I just hope [Floyd] pitches well. I want to try and see if we give Jose the time off from his last start what we get from him.
"It's a tough situation, but I want to see exactly what Jose brings back to the table. Our hope is that Gavin throws the ball well.
"If we have to go with the six-man, I will take that shot. It's late in the season, guys don't have many more days off. In the meantime, I would really like Jose to come back and come back strong."
Guillen is aware that a six-man rotation could affect the normal routine of his starters who normally pitch every fifth day.
"I always respect my players," Guillen said. "I want to do the best for them to perform, but they have to understand our point, what we want to see. We want to see one of the best guys we've had through the years come back and get a shot to perform, and we're going to see one of the kids have a shot to stay in the big leagues.
"We'll be fair with them, and I believe that if that is going to be fair for the ballclub, no one will have a problem. If they have a problem with that I will respect that and we'll see what we can do."
Behind a four-run first inning and seven innings from Javier Vazquez, the Sox (51-59) won their third consecutive game.
"It's a good sign for Javy," Guillen said of Vazquez, who is 6-1 with a 2.70 ERA in his last nine starts. "In the past, he couldn't have won this game without his best stuff."
Jim Thome added his 490th career home run, a solo shot in the second.
The Tigers brought the tying run to the plate in the eighth, but Ehren Wassermann, the Sox's third reliever of the inning, induced Pudge Rodriguez to ground out to third.