Next Friday, Cleveland's self-styled populist mayor, Dennis J. Kucinich, who rose to power in this poor city by blasting its elite, will plead with the uptown bankers to lend the city $15 million in order to prevent it from becoming the first municipality to go bankrupt since the Depression.

Those who know Kucinich intimately realize how distasteful the mayor finds it that he must be beholden to the city's power structure in this way. But the Kucinich administration has become desperate in its battle against a complicated set of financial problems. Finance Director Joseph G. Tegreene has even met with West German bankers, who have offered to find European and Arab investors.

"The issue here is if you can't be saved by Americans, should you be saved by Arabs?" said City Council President George L. Forbes. "A man drowning wants a rope, and I don't think he particularly cares who throws the rope to him. I think that's the position the Kucinich administration has taken."

Tegreene has downplayed the merits of the West German offer, and there have been private rumblings in the cabinet over the involvement of the Arabs because several of Kucinich's top aides are Jewish and the Jewish community helped fill his campaign coffers last year.

The city's major banks, which hold the $15 million in notes that must be refinanced to avoid bankruptcy, have refinanced to avoid bankruptcy, have kept an official silence on their own battle plans.

The bankers are not enamored with Kucinich. They view him as an obstructionist because he opposes such items as tax abatement for new developments. They are still stinging from his blistering charge that Cleveland businessmen are "the most stunning collection of abysmal failures in the United States."

Two weeks ago it was reported that Claude Blair, president of National City Bank, which holds $4 million of the notes, had told associates that he is reluctant to refinance the loans because of Kucinich's antagonism toward business.

Blair denied the report, and the television reporter who made the disclosure quit when the station aired a retraction.

Cleveland's financial problems are complex.

Even if it can refinance the $15 million Friday, it faces default at least three more times next year when another $25 million in short-term notes are due.

The Kucinich administration has proposed a $50 million debt-consolidation bond issue and has recruited Salomon Brothers to head up a syndicate of underwriters.

But City Council has refused to authorize the bond issue, which has been postponed twice already.

The city has had problems meeting stiff financial disclosure requirements, largely because of the city's archaic accounting system. This system is so disorganized that some $52 million in bond funds were diverted to operating expenses without the knowledge of auditors and others responsible for oversight.

Last summer, the city had to buy up some $11 million in short-term notes held by Cleveland banks after they refused to refinance them. At that time, Tegreene was so unsure of the state of city finances that he refused to sign the disclosure statement.

Further complicating the problem is the fact that the city's credit rating has been lowered by Wall Street rating agencies.

Standard & Poor's Inc. suspended the rating, and Moody's Investors Services Inc. has lowered it in steps from A to B.

Jackson C. Phillips, head of Moody's Municipals Division, has been openly critical of Kucinich's handling of finances.

Phillips called them "a crummy bunch" when he said they deceived him on the legality of taking $6 million from a special airport account for general fund use. Last week, Phillips said the financial officials in the administration "don't have the foggiest idea of what they are doing."

The city is left facing a cash shortage the size of which depends upon whom one talks to. Tegreene said the deficit will be around $6 million. Thomas Acklin, a City Council budget analyst, said the red ink will be more than $34 million on a budget of $174 million.

Though all involved are Democrats, Kucinich and City Council have been at war over how to make ends meet.

Kucinich proposed laying off 600 of the city's 10,000 employes, including 250 policemen and 150 firemen. The city already has lost 1,500 employes through attrition in the past year, most of whom have been lost in the safety department at a time when crime and arson rates are soaring.

Kucinich also wants to raise cash by selling city-owned land to the private sector. He has not advocated any increase in taxes.

The council has criticized the layoffs and has blocked the land sales. Instead, it has asked a state court to force the sale of the city's municipal light plant to the investor-owned Cleveland Electric Illuminating Co. for $158.5 million.

Kucinich accused the Council and businessmen of conspiring to force the sale of the light plant and are willing, he said, to bring the city to default "to consummate this crooked deal."