Snyder, an Ironton, Ohio, native and a Marshall graduate, would be introduced at an 11:30 a.m. news conference Thursday in Huntington, W.Va., the source indicated.
He would succeed Bob Pruett, who retired after nine years on the job in February.
Earlier this week, Marshall interim president Michael Farrell had indicated the coaching choice would be introduced sometime this week.
"The search is coming into its final week," Farrell said over the weekend.
It appears that Snyder has outlasted interim coach Larry Kueck, who directed the Thundering Herd through spring football. Marshall wraps up spring drills with a scrimmage Saturday at 4 p.m.
OSU head coach Jim Tressel had made comments publicly and placed phone calls to help promote Snyder's candidacy for the Marshall job.
"Mark Snyder is a perfect fit for Marshall," Tressel said of Snyder's chances for the job. "He's a graduate, he's ready, he's trained hard, he's very talented."
Snyder was a Division I-AA All-American at Marshall in 1987. The Herd was national runner-up in I-AA, losing the championship 43-42 to Northeast Louisiana, and Snyder set the single season MU record for interceptions with 10 that year.
Snyder worked as a part-time assistant at Marshall and Central Florida following graduation in 1988 before landing on coach Jim Tressel's Youngstown State staff in 1991.
He stayed as linebacker coach through 1996, rising to defensive coordinator that final season. Snyder then coached defensive ends at Minnesota from 1997-2000, then rejoined Tressel at Ohio State in 2001 as linebacker coach.
He was elevated to defensive coordinator in 2004, when Mark Dantonio left to become head coach at Cincinnati.
Snyder's departure would leave OSU with just three assistants on the defensive side of the ball -- line coach Jim Heacock, linebackers coach Luke Fickell and newly hired defensive backs coach Paul Haynes.
Those coaches would likely help the Buckeyes complete spring practice, which ends with the April 23 Scarlet and Gray Game.
Tressel could then opt to elevate one of those coaches to the coordinator's role or bring in a new coach to fill that job.
Two names that have been rumored for weeks as Snyder pursued the Marshall job were former OSU defensive backs coach Mel Tucker and former OSU defensive coordinator Gary Blackney.
Tucker left OSU this winter to become the DBs coach on Romeo Crennel's first staff with the NFL's Cleveland Browns. (Tucker is also a Cleveland native.)
Blackney left OSU to become the head coach at Bowling Green and is now an assistant under Ralph Friedgen at Maryland.
Snyder's departure would leave Tressel -- beginning his fifth year on the job at OSU -- with just three coaches from his first OSU staff in 2001. The remaining members of that staff include Heacock (the last remaining holdover from the John Cooper staff), quarterbacks coach Joe Daniels and offensive line coach/offensive coordinator Jim Bollman.