The two-time All-Star left-hander joked he may have something in mind after agreeing Tuesday to a $4.35 million, one-year deal.
"I might ask (Derek) Jeter if I can buy a wing in his house for a little while," Price said, alluding to the 30,000 square-foot mansion that the New York Yankees shortstop owns in Tampa.
The 26-year-old Price, a 19-game winner in 2010, made $1.25 million last season while going 12-13 with a 3.49 ERA to help the Rays advance to the playoffs for the third time in four years.
Center fielder B.J. Upton and reliever Burke Badenhop also agreed to one-year deals before the deadline for teams and players to exchange salary proposals. Upton will make $7 million, and Badenhop will get $1,075,000 next season.
Upton earned $4.85 million last year, when he batted .243 with 23 homers and 81 RBIs. Badenhop was acquired in a trade this winter after the reliever went 2-3 with a 4.10 ERA in 50 appearances for the Marlins.
Reliever J.P. Howell agreed to a $1.35 million, one-year contract on Monday.
The agreements left pitcher Jeff Niemann as the team's only player in arbitration. The right-hander earned $903,000 last season and requested $3.2 million for 2012. The Rays offered $2.75 million.
Price said he was confident all along that his agent, Bo McKinnis, would reach a deal.
"I actually didn't know anything that was going on. I just kind of stayed out of it," Price said. "I have all the faith in the world in my agent. ... He took care of me and got me what I felt I deserved."
The hard-throwing lefty and No. 1 pick in the 2007 draft said he would be receptive to negotiating a long-term deal.
"I love it here. ... It's a good place for me to be," Price said. "As long as I'm here, I'm going to give everything I've got. If we can work something out, so be it. If not, it's part of the business and you just have to take it one day at a time."
Rays executive vice president of baseball operations Andrew Friedman shrugged off a question about whether the team is open to talking about a long-term contract.
"The feelings are obviously mutual in terms of our admiration for who he is and the type of competitor he is, but as far as contract status, obviously those are things we don't talk about publicly," Friedman said.