Sakho has been struggling with a hamstring injury picked up against Chelsea on December 29, while Johnson and Agger are sidelined with ankle and calf problems respectively.
Rodgers confirmed Johnson and Agger are closer to returning to full training than Sakho, but all three will miss the visit of the Gunners.
|25/1||Liverpool are 25/1 with Bet365 to win the title this season|
"Glen Johnson is making a great recovery, so there might be a point towards the middle or end of next week [when he can return]. Daniel Agger will hopefully be next week at some stage.
"Sakho is still out for a little bit, but apart from that we will be the same as what we have been for the weekend."
Liverpool have dropped points at home on just two occasions this season, and Rodgers believes his team rise to the occasion of facing top sides.
"Sometimes I feel, the bigger the game, the better we've played," he added. "At the Emirates though, Arsenal were the better team.
"Every game is critical now before the end of the season. Every team will look to take points off their rivals.
"If we win this weekend, we close the gap on the teams above us. So we need to make sure the performance is right.
"These types of games are an opportunity to make a statement of the progress we've made.
"When I came in, there wasn't much confidence to consistently win. Now there is and none more so than at Anfield.
"We'll respect our opponents, and none more so than Arsenal, but we'll expect to win and have the confidence to do so."