"It's not an easy decision to make," Stoudemire told Yahoo! Sports. "Over time, we will see how things pan out. You give yourself a break during the All-Star break. You think about it with your family. ... That will give me a good solid week on how to weigh out the rest of the season."
The Knicks have had internal discussions about a possible buyout but have yet to approach Stoudemire about it, sources told ESPN.com's Ian Begley earlier this week.
"I haven't talked with Phil [Jackson] or [GM] Steve Mills yet about the future," Stoudemire said Wednesday. "I'm sure we'll have a conversation soon about it."
Stoudemire recently has talked to close friends about the possibility of accepting a buyout from the Knicks but the decision wouldn't be made without "deep thought" from Stoudemire, sources told Begley, because of Stoudemire's loyalty to Knicks owner James Dolan.
"My heart always lies with the Knicks. My loyalty is with [Knicks owner] Mr. [Jim] Dolan," Stoudemire told Yahoo! Sports. "I feel like New York is my home now. I feel like I'm a New Yorker for sure.
"I have a farm here. I have family and friends here. New York will always be my home whether I am here playing for the Knicks or not."
Before Friday's game against the Brooklyn Nets, Stoudemire declined to discuss a potential buyout.
"We'll discuss that after the break. Right now I'm focusing on the rest of the season," he said.
Stoudemire, 32, is halfway through the final season of his contract, and the Knicks are last in the Eastern Conference with a 10-40 record after Friday night's 92-88 loss to the Nets. A buyout could allow him to sign with a playoff contender, although he has played just 33 games this season and dealt with a variety of injuries.
He returned to the lineup Friday after missing the previous four games with ankle, wrist and knee injuries, as well as 14 of the previous 18 games. He had nine points and three rebounds in 18 minutes off the bench.
"All possibilities at this point are still open," Stoudemire told Yahoo! Sports of a possible buyout. "The door is still open for that. But at the same time, I am with the Knicks now. I got to stay optimistic about things and what we are doing here. I can't really focus on the future, because it's not here.
"We still have a couple weeks left before it's all said and done. It's a decision I have to make with my family to figure out the best scenario for the near future."
Stoudemire signed a $99.7 million, five-year deal with the Knicks in 2010 and is set to make about $23.4 million this season, which likely is prohibitive in a trade scenario.
"I don't think there'll be something during this season," Stoudemire said Wednesday when asked about the Feb. 19 trading deadline. "The future is within their hands and in my health. So I just want to make sure I stay healthy and maintain that health throughout the rest of my career, and we'll go from there."
Stoudemire, who spent his first eight seasons with the Phoenix Suns, entered Friday averaging 12.2 points and 7.0 rebounds per game this season, compared to career numbers of 20.1 points and 8.2 rebounds over his 13 seasons.
He hinted at possible motivation for why he might leave the Knicks.
"The toughest part is staying motivated through all the ups and downs, keeping the guys competitive," he told Yahoo! Sports. "This requires an extreme, great amount of perseverance for something like this, especially for me to be 13 years in the NBA and dealing with this type of record. But since we are here, we have to become great leaders, work with the young guys on their mistakes and continue to improve."
In addition to a possible Stoudemire buyout, New York has made it known that point guard Jose Calderon and center Andrea Bargnani are available via trade, sources said. Point guard Pablo Prigioni also has drawn interest from opposing teams, including the Detroit Pistons, according to ESPN.com's Marc Stein.
The Knicks entered Friday with the second-worst record in the NBA. They have endured losing streaks of 16 and 10 games.
Information from ESPN.com's Ohm Youngmisuk and Ian Begley was used in this report.