Sidelined the last couple of weeks with a right Achilles strain, Ortiz and the Red Sox are hopeful that the slugger can return on Wednesday, the first day he is eligible.
"I think he's on pace to back when his [disabled list] stint is over," said manager Bobby Valentine.
Ortiz, who rejoined the team Friday after staying back in Boston for the Texas series, is taking a wait-and-see approach.
"I don't know. Every day is different," said Ortiz. "Every day for me it has been improving. We'll see. If I'm ready to go, I'm ready to go. I want to play."
Missing a series in the Bronx -- where he's had some memorable moments over the years -- pains him.
"Let's not talk about it," said Ortiz.
It's probably no surprise that the Red Sox have struggled to score runs of late without Ortiz.
"It's hard to tell," said Valentine. "We've faced some good pitching and it's hard to tell. You know, David was so on since Day 1 of the season that it's hard to say you haven't missed him. He's pretty good."
Ortiz knows that he'll have to monitor the injury for a while, but he's confident he can play through it.
"It's been a slow process," Ortiz said. "It's something you just need some time off, so probably when I get back I'll probably have to deal with those up and down days. It's fixable -- it just needs some time off."