The four-year deal is worth $28.8 million, with $10.2 million coming in the first two seasons and over $9 million in each of the last two. The fourth season is a team option.
The Knicks would have three days to match the offer after Lin, a restricted free agent, signs.
The Knicks repeatedly have said they plan to keep Lin.
"They will match any offer on Lin up to 1 billion dollars," a source told ESPN.com's Marc Stein.
A report in the New York Post on Wednesday, citing a league source, said the Rockets were planning to offer Lin a backloaded deal worth roughly $30 million.
"Jeremy Lin's an excellent player," Rockets general manager Daryl Morey told the Post. "We got to know him firsthand when he was with the Rockets early this season. We think he'd make a fantastic addition to our team."
The Knicks can offer Lin, a restricted free agent, a four-year deal worth $24.5 million.
While both Lin and the Knicks are hoping for a reunion, sources told ESPN The Magazine's Chris Broussard this past weekend that if a club offers Lin a backloaded contract that pays him an eight-figure salary in the third and fourth years, as Houston has done, the Knicks could be given pause about matching the offer.
With the new collective bargaining agreement employing a more punitive luxury tax, beginning with the 2013-14 season, the Knicks are extremely concerned about the financial ramifications of such a deal, sources said.
The Rockets had Lin in training camp last season, but waived him because they already had Kyle Lowry and Goran Dragic on their roster. Now that they've traded Lowry to Toronto, and with Dragic headed to Phoenix, Houston is trying to get Lin back.
Lin averaged 14.6 points, 6.2 assists and 3.1 rebounds in 35 games with 25 starts before his season was cut short because of surgery to repair torn cartilage in his knee.
Lin, who went undrafted out of Harvard, became a sensation with a remarkable stretch in February, scoring at least 20 points in nine of 10 games. A high point of that span came Feb. 10, when he scored 38 points and had seven assists in a 92-85 win over the Lakers.
The Rockets already are popular in Asia because of the career of former star Yao Ming, who retired in 2011. With Yao's retirement, Lin could add to their appeal there as the first American-born player of Chinese or Taiwanese decent.
Information from ESPN.com's Marc Stein, ESPN The Magazine's Chris Broussard and The Associated Press was used in this report.