The Tigers will bow out of the top flight tomorrow at home to Liverpool after relegation was confirmed by Monday's draw at Wigan Athletic.
Hull are facing an uncertain future both on and off the field with the club's financial problems meaning a fire sale of the high earners is likely.
Stephen Hunt seems certain to leave the KC Stadium during the summer with Wolves back in for a player they tried to sign last January.
Jimmy Bullard is another Hull are desperate to get off the wage bill, while many of the out-of-contract players are also likely to move on.
These include Barmby and Boateng, though Dowie – whose own future beyond tomorrow remains shrouded in doubt – would like to keep both if he stays in charge.
He said: "With all fair weather and things being rosy, Nick and George would be players that you would like to keep around.
"Nick is a vastly experienced player who is great to have around the young lads. George is a leader and a captain – but those will be discussions to be had at a later date.
"I would like to think you could retain them but it is going to be a lot more difficult to retain George than it would be Nick but they are both quality people, not just quality players."
Boateng joined Hull two years ago as Phil Brown looked to bring in Premier League experience following promotion.
The 35-year-old fell out of favour during the second half of last season and was offered the chance to join Ipswich on loan.
This term has been a different story, however, with Boateng being named captain by both Brown and Dowie, who took charge of team affairs in mid-March. Dowie said: "George Boateng is a warrior, that will be his legacy.
"He wouldn't pretend to be David Beckham or Steven Gerrard but he is a warrior who puts his body on the line.
"He is a great character as well. He is upbeat, he is bubbly all the time and he cares deeply about the club. Fans have no problem with the amount of money a player earns so long as he gives everything and George leaves nothing behind.
"Whatever happens, George has been fantastic for me."
Barmby seems to have a more realistic chance of remaining at Hull than Boateng, who is believed to be one of the higher earners following his 1m switch from Middlesbrough in 2008.
Barmby, 36, returned to his home-town club in 2004 and has since helped the Tigers to two promotions.
He has featured in 20 Premier League games this season, though only six of these have been from the start with the most recent coming in last month's 1-0 defeat at home to Sunderland.
It was after the game against Steve Bruce's side that Boateng launched a blistering attack on former Hull manager Brown.
The Dutch veteran blamed Brown for Hull's relegation and cited the infamous on-pitch half-time team talk at Manchester City as the moment when it all started to go wrong for the club.
Asked about Boateng's outburst about his predecessor in the Tigers dugout, Dowie insists he has no problem with his captain's comments. "I am a great believer in speaking your mind. If George had something to say to me, he is always welcome in my office to have a discussion eye to eye.
"I can't comment on who is right and who is wrong but George felt he had to say it. I can only deal with George the footballer and he has been terrific.
"I wish he could have lashed in a volley from 25 yards out but judging by his shooting in training, that is not going to happen."
Tomorrow being the final day of the season, it means a loophole in the football regulations which Hull could have exploited – enabling them to escape a points deduction by going into administration – is about to be closed.
Due to a discrepancy in insolvency policies between the Premier and Football Leagues, Hull could avoid a 10-point penalty next season by calling in the administrators before 5.50pm tomorrow.
A national newspaper last week claimed Hull, whose debt stands at around 35m, were contemplating doing just that, something that the board vehemently denied via an official statement a few hours later.
Instead, owner Russell Bartlett is believed to be fully confident the club can trade through their current troubles.
Meetings have been taking place in the past fortnight to plot a path through the summer and beyond with the Yorkshire Post understanding that the club intends trying to convince creditors to allow extra time to repay money owed. The terms of the club's bank loans could also be renegotiated.
Five moments to savour...
August 18, 2008
Hull City 2 Fulham 1
Caleb Folan ensures the Tigers' first game in the top flight ends in a memorable victory with an 81st-minute winner against the Londoners.
September 27, 2008
Arsenal 1 Hull City 2
The result that made the Premier League sit up and take note of Hull, who became only the second team in 41 games to beat the Gunners at the Emirates Stadium. Daniel Cousin nets the winner.
October 19, 2008
West Brom 0 Hull City 3
A fourth straight win leaves Hull third in the Premier League with 20 points from nine games, only goal difference keeping Phil Brown's men off top spot.
May 24, 2009
Hull City 0 Man United 1
Phil Brown's reaction may have been over the top as the Hull manager launched into an impromptu karaoke session on the pitch but avoiding relegation was a major achievement.
February 6, 2010
Hull City 2 Man City 1
The Tigers follow a midweek draw at home to Chelsea with a stunning victory over the richest club in the world. Goals from George Boateng and Jozy Altidore ensure Emanuel Adebayor's second-half strike counts for nothing.