Grant is desperate to recruit Anelka with Tuesday night's 2-1 Carling Cup semi-final first leg victory over Everton once again highlighting their lack of firepower.
The Blues, missing Andriy Shevchenko and Didier Drogba to injury and Salomon Kalou to the African Nations Cup, were once again forced to rely on the disappointing Claudio Pizarro up front.
Negotiations to take Frenchman Anelka to Stamford Bridge have stalled over Bolton's £15m valuation with the Trotters rejecting Chelsea's initial £11m offer but Grant has targeted a breakthrough by the weekend.
He said: "We have confirmed our interest in Anelka. We wanted him for today and I hope that he will now get him for Saturday.
"If not we'll continue with the players that we have.
"We are missing three strikers so it's important to do something quickly."