The 29-year-old Logan played long toss Tuesday and intends to throw a bullpen session Wednesday, with the hopes of returning to action for Friday's series opener against San Francisco.
"My mind is more at ease now, I'm not too worried about it," Logan said. "Just try to help this team try to get in the playoffs and worry about this when the season is over.
"I'm trying to speed this up. They said I can't hurt myself more than I am. It's OK to go back out there and keep going."
Manager Joe Girardi didn't guarantee that Logan would be back for Friday, but was optimistic that if he passed some hurdles over the next couple days, he would have the lefty for the start of the weekend series, New York's last homestand of the season.
"I think it's definitely a possibility," Girardi said. "After the bullpen [session], we will probably have a much better idea. If he can throw a bullpen [session] on Wednesday, Friday is realistic. I think if he can throw his bullpen [session], then he'll be able to pitch in a game, as long as he wakes up Thursday and feels OK."
Logan said he has dealt with the issue all season long and and it is something he feels more when throwing sliders. The amount of pitches he throws in a given game doesn't cause further problems, he said, but he has decided that offseason surgery is the best course of action.
"I'm tired of feeling like this. I could probably keep going with it but I think it's better to do sooner than later," Logan said about the surgery. "I think it's something I need to do now and be ready for next spring.
"It never hurt. It's one of those annoying feelings. It's one of those pains that you can tolerate it and you're not worried about going out and pitching. But when you feel it every single day of your life, it gets annoying, especially when you don't know what it is. Now knowing what it is, I can deal with it a lot easier, mentally."
The biggest worry, Logan said, is that he's an upcoming free agent and is concerned that the elbow could potentially be an impediment to a contract.
"That's the only thing that bothers me," he said.
Logan has made 60 appearances this season -- trailing only righty David Robertson for the team lead -- and entered play Tuesday with a 5-2 record, with 11 holds and a 3.26 ERA.