The under-the-cap Kings, according to the source, are optimistic Hayes will accept the deal, which would pay the 6-foot-6 forward in the mid-level exception ballpark of $5 million annually.
Said another source close to the process: "Look for [Hayes] to take it."
Hayes has spent his entire six-season career with the Rockets and averaged a career-best 7.9 points and 8.1 rebounds last season, playing nearly 30 minutes per game after the retirement of Yao Ming.
"He's close to gone from Houston," Hayes' agent, Calvin Andrews, told the Houston Chronicle.
Hayes is a native of nearby Modesto and has been pursued hard by the Kings from the start of free agency. That's even after Sacramento's acquisition of another power forward -- J.J. Hickson -- in June to play behind franchise forward DeMarcus Cousins.
Portland, Minnesota, Toronto and Boston are among the other teams to express interest in Hayes besides the Kings.
Marc Stein is a senior NBA writer for ESPN.com.