ESPN Insider's Chad Ford reports that Landry would receive $3 million in each of the three years. However, the Bobcats have a team option on Landry's last season.
The Rockets have a week to decide whether to match the offer or lose Landry to Charlotte.
The 6-foot-9, 248-pound Landry averaged 8.1 points and 4.9 rebounds in 42 games for the Rockets as a rookie last season. Houston extended him a qualifying offer, but the two sides have not been able to reach a deal.
"We saw an opportunity to possibly get a guy that can play both big spots, probably more so the power forward," general manager Rod Higgins said. "He's versatile enough to play the center position in a pinch."
Landry played in college at Purdue. He was drafted by Seattle in the second-round last year, then sent to the Rockets in a deal involving draft picks and cash.
Landry's playing time increased late last season after Rockets center Yao Ming was lost to injury. He scored 22 points in a game at Indiana and was voted to the all-rookie second team.
"It's a shot at improvement," Higgins said. "The clock start now to see if we indeed get the opportunity."
The Rockets have much more depth than Charlotte up front and are also approaching the luxury tax, which could affect their decision whether to match the offer.
It's the second time in a year the Bobcats have tried to get a restricted free agent from another team. In December, Cleveland matched Charlotte's three-year, $17 million deal for forward Anderson Varejao.
The Bobcats open training camp under new coach Larry Brown on Tuesday.
Information from The Associated Press was used in this report. Chad Ford covers the NBA for ESPN Insider.