NEW YORK -- David Price and James Shields visited the MLB Fan Cave Thursday morning in Manhattan, and there was one topic of conversation in the city that dwarfed all others. As it turns out, there is a chance both Rays starting pitchers are right in the middle of it, too.

Price is scheduled to start Saturday at Yankee Stadium. Shields is scheduled to start the series finale on Sunday. After a doubling Thursday, Derek Jeter is two hits away from No. 3,000, so if he doesn't break the mark Friday, that All-Star duo is in line for a possible milestone moment.

"I don't think we care either way," Shields said. "I mean, we don't want to give up hits to anybody, whether it's 3,000 or not, but if he hits it off us, it's not that big of a deal."

"Honestly, I would like to see him do it," Price added. "Just to say that I was there and saw him do it. But I don't want him to get three hits against our team. So I'm kind of in a pickle with that. If it happens, it does. If it does, I'm sure I'll see it on SportsCenter for a long time."

Price already has one Jeter milestone to his own credit. Flash back to Sept. 14, 2008. Price had just reached The Show in his first year, entering the game at Yankee Stadium in relief of Edwin Jackson. Jeter got three hits that day, and that included a leadoff homer in the fifth by Jeter. It was the first hit allowed by Price, who ultimately helped Tampa Bay to a World Series that year.

"My second inning of work, and he goes oppo on me in my debut," Price said. "That stung a little bit."

"Welcome to the big leagues," Shields interjected.

"That's my mom's favorite player, so she was probably happy for him," Price said. "It just upset me a little bit. But it was good. I gave up my first hit to Derek Jeter, and he put me in the record books."

Rookie right-hander Jeremy Hellickson starts Friday.

Price (8-7, 3.56 ERA) and Shields (8-6, 2.47) got the Fan Cave tour with MLB Dream Job winner Mike O'Hara and wingman Ryan Wagner, and then spent an hour filming an upcoming video skit for MLBFanCave.com that is a spoof of a law-firm commercial. In it, the team of Price & Shields promise to help you with pitching problems. They yukked it up through all the takes ("I am such a bad actor," Shields said amid laughter once), a welcomed loose moment for both.

Then it was off to Yankee Stadium and a stretch that is remarkable in its context.

Four games against the Yankees. The 82nd All-Star Game Tuesday in Phoenix, where Price will be available to pitch, but Shields will not. Then three games against the Red Sox. Then four more games against the Yankees. The Rays moved to within three games of the Yankees in the American League East after Thursday's opener, and are 3 1/2 behind the division-leading Red Sox, so this is a huge stretch by any account if you are a professional ballplayer.

"Especially with us being in the All-Star Game together, it's a big moment for us," Shields said. "To be able to go together and be able to spend those moments together, especially the way we grind it out during the season together. Obviously, we have the Yankees, Red Sox and Yankees in three straight outings around the All-Star break. It's going to be a challenge. But we're up for it. We're excited about it and we're going to enjoy the moment."

"That's part of pitching, in the AL East especially," Price said. "You're going to play these teams 18 times a year. There's a good possibility that you're going to have back-to-back starts facing these guys. Not necessarily something you want, but when you can step up in that moment, like Shields did whenever Boston came in and they were so hot, and he threw a shutout against them. When you can do something like that with a team that's going so well, it lets you know where you at."

The pair were the final Major Leaguers to visit the Fan Cave in the first half, bringing the number of players so far to about 50. O'Hara and Wagner will pack up and follow the pitchers to Phoenix, where they will set up "Fan Cave West" poolside, behind the right-field wall inside Chase Field.

"It's well put together. They've got everything they need here," Price said. "It's a place you can come and have a good time. That's for sure. They treated us like family. We came in, did a couple of little spots for our segment, and we had a lot of fun with it."

"We're part of the Fan Cave family now, so it's all good," said Shields, who also brought his wife, Ryane, to the Fan Cave. "They've got pool tables, all kinds of stuff here, a bunch of TVs to watch games. It's pretty nice."