Berlusconi and Mills have previously denied wrongdoing and could not immediately be reached for comment on the prosecutors' request for a trial yesterday.
A judge will now hold a preliminary hearing to decide whether Berlusconi and Mills should be charged and go to trial.
The hearing could start in May, the judicial sources said.
The prosecutors' request for the charges comes a month before a potentially close-fought general election set for April 9 and 10.
Berlusconi has accused Milan public prosecutors of waging a politically motivated battle against him.
The involvement of corporate lawyer Mills in the Italian probe has whipped up a political storm in Britain, threatening his wife's political career after reports said the cash was used to repay the couple's mortgage.
Under investigation
Berlusconi, Mills and 12 others are under investigation in a related fraud case involving the Berlusconi family's media company, Mediaset.
Preliminary hearings to decide whether to indict them began in October.
Mills has testified as a witness at three of Berlusconi's previous fraud trials. Prosecutors have accused Berlusconi of paying Mills the money in exchange for favourable testimony from him in two of those trials.
On Thursday, Milan investigating magistrates rejected a move by Berlusconi's lawyers that would have delayed any request for a trial until after the general election.
"One can only conclude that they (magistrates) want to interfere with the election campaign," Berlusconi's lawyer, Niccolo Ghedini, told Corriere della Sera newspaper.
Jowell was cleared last week of breaching the code of conduct for ministers after she said she was not aware of the $600,000 payment.
But the inquiry by Britain's top civil servant made no attempt to explain how Mills got the money.