Vrabel, 40, just finished his second year with the Texans, whose 9-7 season ended with a disappointing 30-0 loss to the Kansas City Chiefs in the AFC wild-card round.
Head coach Bill O'Brien and general manager Rick Smith worked hard behind the scenes to keep Vrabel and will give him a new contract, the Houston Chronicle reported, citing sources.
Vrabel met with new 49ers coach Chip Kelly on Tuesday before declining the job, the Chronicle reported.
Vrabel previously coached three seasons at his alma mater, Ohio State, before leaving for Houston to rejoin defensive coordinator Romeo Crennel, who coached him in New England.
As a player on the Patriots, Vrabel earned Super Bowl championships in the 2001-02, 2003-04 and 2004-05 seasons. He has earned high praise from New England coach Bill Belichick for his football smarts. In September, Vrabel, a 14-year NFL veteran, was named as one of the 108 modern-day nominees for the Pro Football Hall of Fame class of 2016.
The Texans also hired Anthony Weaver as a defensive line coach, according to the Chronicle.
Why is Mike Vrabel a coveted coordinator?
Mark Dominik reacts to Mike Vrabel's reported decision to decline the 49ers defensive coordinator offer and remain with the Texans.