"We're playing well right now, so I expect to be here," Price told reporters on Monday.
"If we continue to play good baseball the way we have and continue to win, I feel like we have a shot, so I think that would lessen my chances of getting traded."
The trade deadline is July 31. The Rays are 9½ games behind the Toronto Blue Jays in the AL East, and 10 games out of a wild-card spot.
Price, who last week said he was frustrated by trade rumors, can become only the fourth player in major-league history to strike out 10 or more batters in six straight starts when he faces the New York Yankees on Tuesday.
Price leads the American League with 144 strikeouts, including 54 -- with just five walks -- in his past five starts spanning 39 2/3 innings. His velocity is also climbing: In his first six starts, his average fastball velocity didn't reach 93 mph, but in six of his past nine starts, his average velocity has been 93.4 mph or higher.
"If I do get traded, that mound is still 60 feet, 6 inches away from home plate. The bases are still 90 feet (apart). Still nine players on the field. The game doesn't change," Price said. "It's just the uniform I'm wearing might change, and then my teammates. That is a very big deal. But I feel like it's something I can handle."
Still, he doesn't want to go anywhere, but he understands it's "part of the business."
"I completely get that," Price said. "These guys are great owners. They run this to the best of their ability and they've done it extremely well. ... They've put us in position to win whether they kept guys or traded guys."
Rays manager Joe Maddon hopes Price is right, and that he'll keep his ace if the team can get back into the playoff chase.
"I'm looking for us getting extremely toasty right now and getting truly back into this thing from everybody's perspective, and let's run it from there," Maddon said. "It's a lot easier to win it with David being part of the group."