Although after straining his right calf Monday and having to leave the game, Jeter remains six hits shy of 3,000 with the possibility he won't play Tuesday night against the Texas Rangers.
"Hopefully he's either got it by [Saturday], and if he doesn't, hopefully I can keep him off first base," Dempster said Tuesday on "The Waddle & Silvy Show" on ESPN 1000.
Dempster is 4-1 in his last seven starts. He hasn't faced Jeter since 2001, when he pitched for the Florida Marlins. Jeter is 3-for-7 against Dempster with a double, walk and two strikeouts.
"I'm going to let him hit a base hit to right so I can [be a part of] autograph signings with him," Dempster joked. "Look at what it did to Al Downing. He gave up that home run to Hank Aaron, and then he signed a bunch of stuff. I'm sure he probably has a nice new house because of it.
"I'm just going to make pitches to try to get him out. If he gets a hit, he gets a hit. I've never got too upset with guys getting hits, unless they're in big situations. I'm just going to try to make pitches. I'm not going to pitch him any differently than if he had no hits."