The two multi-millionaire businessmen, who made their money out of fish and then oil, are keen to buy into the Maine Road club. Rokke and Gjeltsen own the Norwegian side Molde and already have an arrangement with Wimbledon's majority stakeholder, Sam Hammam.
However, they are not yet investing in the South London club as they believed Wimbledon were going to move to Dublin and become a leading power. Now they could opt to go elsewhere themselves.
The pair, worth an estimated pounds 400m, are looking closely at City, a club they tried to buy during Francis Lee's trouble reign. Rokke and Gjeltsen used the former City player Age Hareide as a go-between in talks with Lee a year ago to set-up a financial injection.
Hareide was then the coach of Molde and would have been installed as first-team coach at City. There would also have been a transfer agreement between the clubs.
The deal was called off because Lee was unwilling to show the Norwegians the club's books and they turned their sights to Wimbledon instead. Now the Dons' plan to move to Dublin is on hold and the Norwegians could pull out and put their money into City instead.
City yesterday announced a pre-tax loss of pounds 6.3m for the year to 31 May. The accounts also show a loss on transfers of almost pounds 2m and a wage bill on players and staff of pounds 8.7m, up by pounds 1.5m on the previous year.
Since May the overall playing staff has been cut from 52 to 37, and the club's payroll list from 160 to 141. In his report, the chairman, David Bernstein, said: "Turnover is up 20 per cent to pounds 15.3m, which is healthy. But we have an unacceptable level of expenses arising largely from the size of the playing staff and resultant wages."
However, a financial boost for the transfer budget and the prospect of moving to a new ground makes the club the type that could be floated in the near future and that also appeals to the Norwegians.
Joe Royle, the City manager, is trying to bring Mike Sheron back to Maine Road and end his miserable time at Queen's Park Rangers. Royle wants Sheron on loan for his Second Division side and the striker would be keen to rejoin his first club. Sheron has had a fall-out with Rangers' player- coach, Vinnie Jones, and sees little future at the Loftus Road club, who would also like him off their wage bill.
Chris Sutton will have X-rays today amid fears that an ankle problem could put him out of the Blackburn Rovers team for the next few weeks.
Sutton has been struggling with the injury, needing regular treatment that has kept him out of training and forced him to have the problem analysed.
The Rovers manager, Roy Hodgson, will be anxious that Sutton be proved fit as his forward line is already weakened ahead of the Premiership match with Everton tomorrow.
Sutton may even be forced to play if the X-rays do not show any bone or ligament damage because Kevin Davies is sidelined after tonsilitis. Kevin Gallacher is recovering from a calf injury, leaving Martin Dahlin as the only fit striker at the club as difficulties mount for Hodgson.
The Wolves midfielder Steve Froggatt looks set to join Coventry City for pounds 2m. The Highfield Road club had a pounds 1.5m bid for the former England Under-21 international turned down earlier this month and Middlesbrough have since joined the bidding.
The Dutch goalkeeper John Achterberg is set to make his debut in goal for Tranmere Rovers at home to Swindon tonight, after arriving from FC Eindhoven on a free transfer. He will replace Steve Simonsen, who has joined Everton. Danny Coyne, the other recognised Rovers keeper, is absent through injury. Mike Walsh, the former Bury manager, will take caretaker charge of Swindon.