Manager Jim Leyland said Valverde, who suffered a lower back strain Tuesday at Chicago, was feeling better Saturday and will play catch again Sunday morning.
"If he felt great, he may be available," Leyland said, "but I kind of doubt that. I kind of think maybe Tuesday in Cleveland. I can't swear to that though."
Jackson, too, said Saturday he was feeling more improvement from the abdominal strain he suffered Wednesday night against the Twins. He was going to try take some swings off a tee to see how he felt.
"The main thing is to see how far I can go with it and get a gauge from that," Jackson said.
If he feels well enough, he didn't rule out some limited availability Sunday.
"If I get out there and feel pretty good, I may be available to run if that [situation] presents itself," he said.