Murray had been leading the line for the Seagulls but picked up a problem in the defeat to Leicester City, keeping him on the sidelines for three weeks and allowing Israeli striker Hemed to steal a march on him.
Hemed was on target last Saturday when Brighton recorded their first win of the season over West Brom, Murray stepping off the bench to replace him not look after he had struck.
Boss Chris Hughton is likely to keep faith with Hemed for Friday's clash at Bournemouth, meaning Murray will be on the bench against his former club, but the 33-year-old says he is now ready to turn up the heat on his team-mate.
"I just need to get some training under my belt and get back up to speed," he told the Argus. "I lost a little bit of fitness during my three weeks out, so I just need to keep at it, look to get back into the team and push Tomer.
"I thought he did well in the West Brom game, the whole team played as a unit and we looked a lot more comfortable.
"We showed that we’re capable of winning games at this level. Leading into the first international break, it was a learning curve for us.
"During that learning curve we built confidence and belief in each other, and I think it all came together against West Brom."