An independent committee whittled a list of 100 possible designers down to two following an open competition.
But the eight members are evenly split over who should be the winner.
The final choice is between the "avant-garde" Bombay-born British Turner Prize-winner, Anish Kapoor, or a "restrained" design by American landscape architect Kathryn Gustafson.
Chairman Rosa Monckton, a close friend of Diana, used her casting vote in favour of Gustafson, but Kapoor's supporters complained.
An unnamed source told London's Evening Standard newspaper: "It was a classic split between the avant-garde and the rest.
"Rosa Monckton wanted something that she believed the princess herself would have liked.
'Shocking'
"The ultra-modernists wanted to make a statement for British art."
Kapoor's design is said to be "possibly shocking" while Gustafson's is described as "restrained and elegant".
The memorial fountain committee was set up in December 2000 to oversee the project and reports to the Diana memorial committee chaired by Chancellor Gordon Brown.
Fountain timeline
Diana died Aug 1997
Permanent memorial fountain announced Sept 1999
Design competition launched Sept 2001
Design shortlist chosen Dec 2001
Design reportedly chosen Jan 2002
Committee deadlock July 2002
Ms Jowell said: "The committee asked me to find an appropriate way forward in the face of their impasse.
"As the minister responsible for the project, I will be considering their views and recommending a winner."
The monument will be situated beside the Serpentine Bridge in Hyde Park.
Work to build the fountain will begin immediately, but it may be difficult for the government to honour a pledge to build the fountain before the sixth anniversary of Diana's death in August next year.
Last month, a frustrated Ms Jowell was said to have been "greatly concerned" over delays in commissioning the fountain.