The Telegraph reports that United plan to make the bid for Fellaini before the clash with rivals Liverpool at Anfield on Sunday.
United failed with a combined bid of £28million for Fellaini and Leighton Baines last week, but are now ready to make a renewed bid.
Fellaini had a £23million escape clause in his contract, but that clause expired at the end of last month.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.