The Trotters were condemned to spend next season in the Championship following their 2-2 draw away at Stoke City last Sunday, ending their 11-year spell in the top-flight.
However, Coyle, who played for the club between 1993 and 1995, has received full backing from the chairman.
"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."
|20/1||Owen Coyle is 20/1 with William Hill to be named as Aston Villa's next permanent manager.|
Coyle took over the reins at the Reebok Stadium in January 2010, leading them to two 14th-place finishes during the next 18 months.
But, despite finishing 18th this season, Gartside does still have faith in Coyle, insisting mounting injury concerns among the squad contributed to their downfall.
He continued: "He's been very unlucky this year. He's a young manager, he's learned a lot and we've invested in that."
"The experiences we've all had this year have been unique and unprecedented. These are not excuses, they are reasons."
"During the season, we've had 15 trauma injuries, including four broken legs. I've been on board for nearly 30 years and I've never seen a season where we've had such a horrendous injury list."