Ortiz, who has been bothered by an Achilles injury since July 16, said a decision will be made by the end of the day after Ortiz meets with medical personnel.
"We're talking about it because I can't really play like this," Ortiz said. "I don't want to be thinking about my foot while I'm facing the opposition, which is what happened to me after I hit that double [Friday night].
"My last two at-bats -- instead of focusing on seeing the ball and hitting it -- I'm thinking about how my foot is going to react once I take off running," Ortiz added, referring to two strikeouts.
The slugger had a closed-door meeting with general manager Ben Cherington and manager Bobby Valentine after Saturday night's game.
"I just want to make sure I'm 100 percent," Ortiz said. "If I'm good, I'm good. I love being on the field and doing my thing, but you've got to be ready for that."
Valentine would not elaborate on the particulars of the get-together, only saying that Ortiz "didn't think today would be a good day to play."
Sunday marks the second straight game Ortiz has missed since coming off the disabled list Friday, a return that may end up consisting of one game if the soreness does not go away.
Valentine, speaking before Ortiz did Sunday, indicated the decision may come a little later.
"We're probably there. We're just going to give it a couple of days to see," Valentine said. "He said that the practice and game, there's just that little level of adrenaline that differentiates. And when he hit that double [Friday night] and he turned to second, he was uncomfortable, where he was comfortable doing those things in practice.
"We're definitely not going to do anything to jeopardize David's career. David totally wants to do everything he can to be part of this team this year and in the future. So that's what we're dealing with."
Before his injury, Ortiz was having his best season in years, hitting .318 with 23 home runs, 60 RBIs and an 1.026 OPS. With Saturday's loss, the Red Sox are 14-23 without Ortiz in the lineup. They are 46-44 in games in which he has appeared.
Asked if the Red Sox falling out of contention is a factor in his decision, Ortiz said: "I don't really care about that. I want to play. When I'm good, I like to play no matter what the situation is. It's not the first time we're out of contention and I'm not shutting it down for any particular reason. I like to play. I like to be on the field.
"I know the fans like to come and watch me play. It's our job, when we're healthy, to be on the field --no question. There's nothing else I'd like to do more than be on the field. I enjoy that but you've got to be healthy for that."
Of the pain he felt in the Achilles after his double on Friday, Ortiz said, “I was definitely feeling better and wanted to give it a try just to see how things go and being back in the lineup to help things get better. Game intensity is different than getting ready to play. Your body normally does different things when somebody’s trying to get you out than just running on your own. I’m getting better but I’m not ready yet.”
“I’m on my way to where to be what I want to be, but it takes more time and takes a different process that I’ve got to approach. It’s either that or it’ll get worse and I’m not planning on getting worse.”