The Chelsea owner drove through the record-breaking signing of the striker from Liverpool in January in the hope that he would make the club a force in Europe.
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No way: Fernando Torres sees his shot saved by Wigan goalkeeper Ali Al Habsi
But after losing to Manchester United in the first leg of their quarter-final in the Champions League last Wednesday, Abramovich's patience is wearing thin.
A Chelsea insider said: 'I know the owner is not happy with his investment. He could even sell Torres in the summer, despite having just bought him.'
Sir Alex Ferguson's side went 10 points clear at the top yesterday with a 2-0 win over Fulham.
Torres has failed to score for Chelsea despite spending 648 minutes trying and he squandered good chances when he came on against Wigan yesterday, as Carlo Ancelotti started with Didier Drogba in a 1-0 win.
Way to go: Torres last found the net in Liverpool's 3-0 win over Wolves in January
He has looked a shadow of the player who took the Premier League by storm at Liverpool and Abramovich is aware that interest in the former Atletico Madrid player remains strong in Spain.
It would be a climbdown for the Russian to give up so soon but he will listen to offers if he sees no improvement before the end of the season.
Chelsea have struggled with Abramovich-led buys before, with ?30m Andriy Shevchenko failing at the club and his presence adding to problems with then manager Jose Mourinho.
But Ancelotti said: 'Everyone here wants him to score. The goals will come, maybe at Old Trafford, who knows?'
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Explore more:People: Alex Ferguson, Didier Drogba, Roman Abramovich, Fernando Torres, Andriy Shevchenko, Jose Mourinho, Carlo Ancelotti Places: Liverpool, Spain, Europe