"I hope that he's here managing," Dempster said Wednesday on "The Waddle & Silvy Show" on ESPN 1000. "I think that he has done a great job. I know he knows the game of baseball really well. He's a really good baseball man. We've all enjoyed having him so far, and hopefully he's given a real good shot to manage because I'd like to see him be our manager for sure."
The Cubs, who have won eight straight road games after beating the San Diego Padres on Tuesday night, are 21-11 under Quade.
"I think he's very good at talking to people," said Dempster, who improved to 15-11 with Tuesday's win. "He knows us all really well. He's been a great communicator so far ... He's done a really good job as far as letting guys know when they're playing, when they're doing well. He's going to be the first guy to jump somebody's seat if they didn't do something right, but he's also going to be the first guy to pat them on the back and tell them what a good job they're doing."
Quade appreciates the support from his players. He believes it has much to do with the on-field results.
"I think, if we hadn't been winning during this time, who knows what the comments would have been," Quade said before Wednesday's game in San Diego. "No matter what the situation, winning takes care of a lot of stuff. Things are never perfect, even when you win. But it does make for a lot better environment, for sure.
"I got an opportunity to come in and do things the way I like. And [GM] Jim [Hendry] gave me free reign to take the shot and go do it. Nothing's gotten in the way of me being able to do that, and the results have been good. "
Although Dempster would like to see Quade back, he said he will gladly play for anyone the Cubs hire.
"I like whoever they are going to bring in. I mean that," Dempster said. "I think whoever ends up being the manager for next year is going to be a good choice. All I'm saying is that I'd like to see Mike as our manager because he's done a really good job, and I've always enjoyed having him as a coach. He's into every pitch of the game."
Cubs broadcaster Bob Brenly and former Florida Marlins manager Fredi Gonzalez withdrew from consideration for the Cubs job. Cubs Triple-A manager Ryne Sandberg and former Cleveland manager Eric Wedge are the only two known to have interviewed for the position. Cubs general manager Jim Hendry is still planning conversations with Washington coach Pat Listach, former Arizona manager Bob Melvin and former Seattle Mariners manager Don Wakamatsu.
Hendry is expected to interview Quade after the season.