Liverpool have agreed to sign central defenders Mamadou Sakho and Tiago Ilori for a combined fee of around £25m.
Sakho, 23, who can also play on the left and has 14 France caps, will cost £18m from Paris St-Germain with Ilori, 20, moving from Sporting Lisbon.
The duo, who have undergone medicals, are set to be at Anfield for Sunday's league match against Manchester United.
Liverpool are increasingly hopeful of adding Chelsea winger Victor Moses on a season-loan long as talks continue.
A deal to take keeper Shay Given on a one-year loan from Aston Villa as back-up to Simon Mignolet is, however, likely to go to the wire on deadline day.
Cissokho sustained an ankle injury in Tuesday's 4-2 extra-time Capital One Cup second-round victory over Notts County at Anfield, in which he was making his first start since joining on a season-long loan from Valencia.
"He could be four to six weeks, which is a blow because he came in and trained really well last week," said Rodgers.
"But he is on crutches at the moment and we'll look at that over the coming weeks. He certainly won't be available [against Manchester United]."
There was, however, better news on fellow defender Kolo Toure, 32, who was carried off on a stretcher with a groin problem against Notts County.
"Toure's injury is nowhere near as bad as we thought," added Rodgers. "We will assess that over the next 24 to 48 hours. We were all thinking he might be out for longer but he's made an excellent recovery.
"The diagnosis isn't anywhere near as bad as we thought, so we'll see how he is for this weekend. If it's not this weekend, then after the international break he won't be too far away."
Meanwhile, midfielder Joe Allen, 23, who also suffered a hamstring injury in midweek, will soon be back in action.
"It was only a grade one strain, so he may be doubtful for the weekend but certainly after the international break, he'll be fine," said Rodgers.