Schneider said "a number of clubs" inquired about acquiring Thomas, and the NFL Network reported that the Cowboys decided that dealing a second-round pick for the safety was too much.
"My sense is that he wants to be here," Schneider said in an interview on 710 ESPN Seattle. "I haven't got that sense (that he wants to be traded) from his agents at all."
The 28-year-old Thomas, a six-time Pro Bowl selection, is scheduled to make $8.5 million on the last year of his contract this season and Schneider said last month he does not expect the eight-year veteran to hold out for a new deal.
Schneider said he expects Thomas to be an integral part of a restructured Seattle defense.
Thomas has made 642 tackles, 25 interceptions and five fumble recoveries for Seattle after being selected by the Seahawks with the 14th pick in the first round of the 2010 NFL Draft out of Texas.