Cahill has been a regular goalscorer against their near-neighbours in recent matches but is currently on Asian Cup duty with Australia.
However, Osman insists back-to-back wins shows they can cope without their goalscoring midfielder.
"Possibly we'll miss Tim Cahill but he has been away for two games now and we've won them both so we're not in any way sitting and being upset about him not being here," he told the Liverpool Echo.
"We're aiming to do the double in the derby matches this season. We've got to concentrate on ourselves and make sure our form is right, and we turn up on the day ready to take three points."
Source: PA
Source: PA