French Finance Minister Christine Lagarde's chances of leading the IMF improved on Tuesday, as France claimed China would back her, even though she faces allegations of abuse of power at home. The 55-year-old former corporate lawyer, a close ally of President Nicolas Sarkozy, had not formally applied for the job, but is regarded as a frontrunner and has the backing of European heavyweights France, Britain and Germany. This despite the fact that the last managing director of the fund, Dominique Strauss-Kahn, was also French and left under a cloud after he was arrested in New York and charged with a brutal sexual assault on a hotel maid. The International Monetary Fund, lender of last resort for cash-strapped governments, is traditionally led by a European, but some of the world's faster growing emergent economies were thought to have wanted to take their turn. Nevertheless, French government spokesman Francois Baroin said that the largest emerging power of then all would not stand in Lagarde's way. "The Chinese are favourable to the candidacy of Christine Lagarde," he told Europe 1 radio, without confirming that she would be a candidate. Asked about Baroin's statement, officials at China's central bank declined to comment. Last week, the bank said the IMF leadership should "better represent emerging markets," without suggesting a candidate. "What is being drawn up is a European consensus," Baroin said. "But you will easily understand, given the circumstances of the IMF director's resignation, and given that it is not a point of national pride, that it is not for France to take a position first. "We do not want to make any gesture that could be interpreted as a form of contempt for emerging countries nor any sign of arrogance, given the circumstances," he said, in a tacit nod to the shaming of Strauss-Kahn. Lagarde is widely tipped as favourite  a European Union source on Friday dubbed her "practically a shoo-in" but has not confirmed her interest. She is not an economist but, having lived and worked for many years in New York as a corporate lawyer, she is a fluent English speaker and is respected in international circles. Before being recruited by Sarkozy's centre-right government she was not seen as a politician, but she is seen in France as a free market champion. Asked on US news channel CNBC on Monday what she would say if offered the post, she replied: "I'd say what an interesting question, but clearly premature. It's for others to decide, my dear." She has received enthusiastic backing in many European capitals, but some in Paris worry that a judicial investigation into a possible abuse of power in her current position could end up ruling her out. Legal sources told AFP on Tuesday that judges would decide on June 10 and not before whether or not to allow the probe which could lead to criminal charges and even a jail term -- to go ahead. This date, which coincides with the closing date for IMF candidacies, is the next meeting of which the complaints commission of the Court of Justice of the Republic, charged with deciding whether serving ministers can be probed. Lagarde's authority had been undermined by allegations she exceeded her authority by cutting short a legal battle between French tycoon Bernard Tapie and a state-owned bank and sending the parties into binding arbitration. The arbitration panel decided to award Tapie 385 million euros over the bank's alleged mishandling of his sale of the Adidas sportswear firm. Prosecutors have asked the court to decide whether Lagarde can be formally investigated on charges of exceeding her authority. It could throw out the case, it could ask for more information or it could order an inquiry which in turn could see Lagarde charged.