Rodgers has splashed some £100m this summer, but admits that there is still money available to recruit a "top-level striker" to replace the Uruguayan, who hit 31 goals last season.
"The money is there - and we will look to improve at the top end of the field until the very end of the window," Rodgers told reporters.
"It's not easy to get a top level striker, no. But we have to keep looking. We certainly need something, because we haven't brought in another striker so far, apart from Rickie Lambert.
"You just never know what will happen in that last week - the window will always throw up something."
Belgium striker Divock Origi, who joined the Anfield club in the summer, will play the duration of the 2014-15 campaign on loan with French club Lille.