Sources close to the situation told ESPN.com that the Grizzlies have offered Gay a five-year contract worth just over $80 million and that Gay has verbally accepted the deal.
"It's as close as you could get," one source said. "The deal will be consummated."
The deal will pay Gay more than $13 million starting next season, with annual raises of 10.5 percent, a definite upgrade over the five-year, $50 million offer he turned down last season.
Another source said Gay is canceling scheduled meetings, such as Thursday night's planned visit to Minnesota, which all but confirms that the restricted free agent is staying in Memphis.
A deal cannot be formally signed until July 8 -- which is the first day that players and teams can execute new contracts -- but sources said Gay and the Grizzlies quickly came to terms within the first 12 hours of free agency.
Although Grizzlies owner Michael Heisley has vowed for weeks to match any offer sheet Gay receives, that did little to dim the expectation around the league that Memphis would ultimately lose him, with Minnesota, New Jersey and the Los Angeles Clippers among the interested.
But once the Grizzlies nudged their contract presentation past the $80 million mark, outside bidders couldn't top them, even with a front-loaded offer sheet.
Gay averaged 19.6 points on 46 percent shooting along with 5.9 rebounds last season and was widely regarded as one of this summer's 10 most coveted free agents.
Marc Stein is a senior NBA writer for ESPN.com. Information from The Associated Press was used in this report.