Dowie was appointed on a short-term contract to replace Phil Brown in March but the former Charlton boss failed to arrest the Tigers' slide towards relegation.
Dowie, whose deal runs out in a week's time, and chairman Adam Pearson have both stressed sorting out the club's financial troubles must take precedence over appointing a manager for next season.
The 45-year-old has not been a universally popular appointment with Hull fans but Barmby has been impressed by Dowie's approach and would like to see him given another chance.
"His intentions and ideas are good, he's very professional," Barmby said. "I've got on with him well and I've been impressed by him. If he gets the job, great, if he doesn't then I'm sure he'll get another job."
Barmby is one of a handful of Hull players who are out of contract at the end of the season.
The 36-year-old joined his hometown club six years ago when they were in the third tier of English football and helped them win promotion to the top flight for the first time in their history, and he is keen to extend his stay by another year.
Pearson has already stated his aim of reducing the wage bill from £39million to around £15million, meaning Barmby would almost certainly have to take a wage cut.
"I'll sit down after the season and speak about that," continued the midfielder. "We've talked briefly but he (Pearson) has got a lot on his plate.
"Obviously I'd like to stay but we'll see how it goes. I've felt good this season. I've been available for every game other than one so hopefully I can go on for another year."
Hull's relegation was all but confirmed with defeat by Sunderland two weeks ago, and after the match midfielder George Boateng hit the headlines by blaming Brown for the club's relegation.
Barmby said of the Dutchman's outburst: "I wouldn't say anything like that. If you have your beef with your manager then, for me, it's between us.
"But George felt he had to say something, he wanted to get it off his chest and that's the way George is, and everyone knows that. Phil Brown certainly knows that - it's probably why he bought George. He's been fantastic for us this season and last season."
Boateng claimed team spirit had suffered and that the squad were not together, but Barmby disagrees.
He said: "We've always gone out on the pitch to give our best and to win the game. The spirit has always been there among the players since I've been at the club, that's never been a problem, but people have different opinions."
Hull end their two-year Premier League stay tomorrow against Liverpool at the KC Stadium.
Dowie is again set to give a chance to youngsters Tom Cairney, Mark Cullen and Will Atkinson, who all started the 2-2 draw against Wigan last week.
Cullen and Atkinson scored their first Premier League goals and, although the result was not enough to prevent Hull's demotion being confirmed, Barmby saw plenty of positives for the future.
He said of tomorrow's match: "We want to put on a good performance for the fans. Hopefully the young kids will play. They'll be itching to pit their wits against one of the best teams in the country.
"They've been knocking on the door and whenever there's a negative there's always a positive, and that shining light could be the young kids, as long as they apply themselves right on and off the pitch. They're good lads and they've got good ability."
The clash could have been key at both ends of the table but Liverpool have endured a disappointing season and can finish no higher than sixth.
Barmby is saddened by the decline of his old team but is confident they can reclaim their top-four spot.
He added: "If you lose your best players, no matter who you are, you're going to struggle. It's disappointing to see them where they are because they are a top-four club. It'll be a tough season next season for Liverpool but they'll bounce back, I've no doubt."