Recent reports had claimed that Coyle may leave the Reebok Stadium following Bolton's relegation to the Championship on Sunday afternoon.
However, Gartside believes that the Scottish boss will remain in his position as Wanderers bid to make an instant return to the Premier League.
"I want Owen to stay and I'm certain he will stay," Gartside told BBC Radio Manchester. "We've formed a good working relationship and I respect the way he works.
"He's been very unlucky this year. He's a young manager, he's learned a lot and we've invested in that."
Coyle took over Bolton in 2010.