Sturridge recently suffered a thigh injury which will keep him out for a further six weeks as he was on the road to recovering from a calf strain, which followed on from another thigh injury.
Liverpool signed Origi in the summer from £10 million from Lille, but had to loan him back to the Ligue 1 club in what appeared to be something of a deal breaker. Reports in the last few days suggest the Reds are prepared to pay an extra fee to allow him to join in January.
The Liverpool boss said: "He's a young player we signed last summer was on agreement he had to stay at Lille.
"That was one of main reasons we were able to sign him. As far as I'm concerned that's still case with Origi."
Rodgers said Sturridge was 'as down as he'd seen anyone' when he picked up his latest injury, saying he just wants to play football.
"Daniel has just been extremely unfortunate. He's a player who doesn't want to be out for this period of time with the quality he has."
Mario Balotelli is expected to be assessed ahead of Sunday's trip to Selhurst Park where the Reds take on Crystal Palace after he returned from international duty early with a hamstring injury, but Rodgers said Rickie Lambert will 'feature heavily' over the coming fixtures after making only the three starts since his summer arrival from Southampton.
His strikers have been under fire in the absence of Sturridge, but the Liverpool boss defended them, saying: "I have great trust in the players. I would be more concerned if they were moping around or didn't care."
One man who should be fit for Sunday's clash is midfielder Jordan Henderson who picked up a hamstring problem on international duty and wasn't risked for England's 3-1 win over Scotland on Tuesday.
It has been a difficult period for the Reds at the start of the season but there are a number of winnable games coming up, coupled with two crucial Champions League games which could make or break their season, and Rodgers seems keen to take the pressure of the players a little.
He said: "A key feature for us has been the spirit we've built up over the past couple of years here. Players are giving me everything.
"I'm not dogmatic. We've played various systems in my time here. We will always explore different options. That's my job as manager."