"We'll make that decision on Wednesday," Gruden said when asked whether Griese would start in Week 6.
Griese, 3-1 as the starter, completed 13 of 19 passes for 88 yards at Denver. Garcia was 13-of-17 for 93 yards, one touchdown and one interception in his first action since struggling in a loss at New Orleans on Sept. 7.
Gruden was noncommittal about whether Garcia played well enough to regain his job even if Griese, who beat Chicago and Green Bay the previous two weeks despite throwing six interceptions, can play this week.
"Obviously, health is going to be an issue," Gruden said. "Jeff did some good things. His health has been an issue, and his return to health is something we're excited about."
Also, pat-down searches of fans entering Raymond James Stadium will resume Sunday.
The searches were suspended in 2005 pending a lawsuit from a high school civics teacher and season-ticket holder. Gordon Johnston argued the pat-downs violated constitutional protection against unreasonable searches. A state circuit judge and U.S. district judge agreed with him.
But the 11th Circuit Court of Appeals in Atlanta ruled in June that the district judge erred in allowing the injunction to remain and that Johnston's lawsuit was without merit because he consented to the searches.
The court's opinion further stated that Johnston knew he would be searched and that the process "supported a 'vital interest' to guard against mass casualties at NFL games from a potential terrorist attack."
The Tampa Sports Authority filed a motion last month to dissolve the 3-year-old injunction preventing the searches, which also are performed at other NFL stadium gates as part of the league's security procedures.
Fans attending Super Bowl games have been subject to pat-downs since 2002.
Information from Reuters and The Associated Press was used in this report.