Carlo Ancelotti is giving Chelsea owner Roman Abramovich a problem.

All informed reports suggest the Russian billionaire is set to make Ancelotti his next ex-manager this summer, but Chelsea keeps winning. Wednesday’s 3-1 victory over Birmingham saw the Blues move above Arsenal into second place, six points behind Manchester United, which must play both the London powerhouses in the coming weeks.

Could Abramovich really sack Ancelotti if Chelsea retains its title?

At any other club the question would not even be asked, but Abramovich is a man unbothered by compensation and has shown to have bouts of unpredictable knee-jerk reactions.

Chelsea, six wins from its last seven league games, plays relegation-threatened West Ham Saturday after United takes on in-form Everton.

On Sunday, Arsenal travels to Bolton where it can expect a reaction from the home side’s 5-0 thrashing by Stoke in the F.A. Cup semifinal a week ago. Most neutrals would consider a humble bet on Chelsea winning the best investment.

Ancelotti appears to have, at least temporarily, given up on £50 million Fernando Torres, whose appearances as a substitute against Birmingham made it 13 games and almost 900 minutes without a goal since his transfer from Liverpool.

The Italian has restored Didier Drogba to the focal point of the attack and he is showing all the hunger, passion, power and leadership qualities lacking in Torres’ game.

As much as anything the team seems more comfortable without Torres and has belatedly displayed the qualities that saw it complete the double last season. Even if Chelsea (or Arsenal) wins every game, it still needs United to slip up elsewhere, with Everton the chasing pack’s best hope of upsetting the Reds.

United also has the distraction, albeit one Chelsea and Arsenal would like, of a Champions League semifinal against Schalke. Manchester City showed in the F.A. Cup semifinal that United is beatable, and how impotent it was without the suspended Wayne Rooney, who is available again against his former club Everton.

One thing is clear: Chelsea will not relinquish its English crown without a fight even though Ancelotti conceded: “I would rather be in United’s place.”

Chelsea has banned further questions about Ancelotti’s future but there is little more he can say. He has given the impression of someone who knows his days are numbered, his philosophical attitude no doubt influenced by the £5 million payoff he would receive.

It is difficult to find anyone who believes Ancelotti is not the right man for the job, though in the past week Harry Redknapp, Jose Mourinho, Frank Rijkaard and Marco van Basten have all been “set” to take over this summer according to various “exclusives.”

Abramovich, or rather his millions, have made Chelsea into the force it is, but he appears to be so obsessed about winning the Champions League he will continue to fire managers until his ambition is achieved.

ARSENAL, YET again, showed it lacks the backbone to be the champion by throwing away leads against Liverpool and Tottenham. The 3-3 draw with Spurs on Wednesday was the game of the season, with Arsenal playing some breathtaking football. But its display at White Hart Lane mirrored a season of frustration and underachievement.

With Samir Nasri and Theo Walcott running riot, the Gunners led 3-1 after 40 minutes. Yet again they were unable to hold on to a lead and see the game out, the second time this season they have squandered a two-goal advantage against their North London rivals.

They were also ahead against Liverpool last Sunday, almost impossibly, they threw away a four-goal lead at Newcastle and they lost the League Cup final 2-1 after scoring the opening goal against Birmingham.

The current Premier League is not one of vintage quality, and Arsenal, five draws in its last six matches, looks like it has missed a golden opportunity to win the title.

In contrast, Spurs have picked up 22 points from losing positions this season.

Under Arsene Wenger, Arsenal has played the best football in England, but six years without a trophy (assuming it does not win the title) has understandably seen some of his methods questioned. Arsenal has the beauty, but it also needs some of the best players like Tony Adams, Martin Keown and Patrick Vieira provided.

The frailties that are obvious to others have been ignored by Wenger. Arsenal looks to have a goalkeeper of stature in Wojciech Szczesny, but Wenger should have invested in a top-class e_SSRqkeeper rather than persist with Manuel Almunia for the last three years. Wenger has signed cultured, ball-playing defenders who lack the physical or mental strength John Terry gives Chelsea or Nemanja Vidic gives United.

Producing players rather than buying them is an admirable policy, but Wenger has failed Arsenal by not investing in a superstar or two. It is difficult to think of anyone who could do a better job for Arsenal than Wenger, though the Frenchman needs to change his transfer policy or else the years without a trophy will continue.

Wenger, the Arsenal players, the Arsenal fans . . . just about everybody knows the Gunners appear to have thrown away a Premier League title that was well within their grasp. Six years and counting.

Christopher Davies was a longtime Premier League correspondent for the London Daily Telegraph.

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