"I'm very confident I will be on the mound this season, whether it's next week or the week after -- I need to consult with the doctor, the trainer and the club," said the 38-year-old Saito.
Saito said a Sunday bullpen session was something of a breakthrough in his rehabilitation.
"If they asked me to throw better than that, it would have to be in a simulated-game situation to hitters," he said. "I know it's going to be tough from here on, but I see the light at the end of the tunnel. I have to be really conservative, really cautious, but I'm very optimistic.
"I was able to throw my fastball yesterday as confident as I probably can and today played catch on flat ground, and I was able to throw long distance, about 120 feet. That boosted my confidence."
With no elbow pain after the Sunday bullpen session, Saito took the next step in his recovery Monday, beginning to throw about 20 breaking balls on flat ground, and he said there again was no discomfort.
"This guy is getting excited," manager Joe Torre said. "Until he throws the slider, we can't count on anything."
With Saito out, Torre has used Jonathan Broxton as the primary closer with Hong-Chih Kuo setting up.
Torre said Brad Penny continues to throw on flat ground but not yet off a mound, so his return isn't imminent. But at least it's still a possibility, which isn't the case with Jason Schmidt, who Torre said has been shut down for the rest of the season. Schmidt, unable to return from shoulder surgery performed 15 months ago, was not available to discuss his options, which might include another operation.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.