He has scored 11 goals this season, helping to elevate Liverpool into second place in the Premier League.
Sturridge damaged ligaments in his right ankle playing for England in a friendly against the Republic of Ireland last June. He was able to return for the start of the season after two months of rehabilitation.
Rodgers would be forced to change formation should he be without the England striker, with the onus falling back on Luis Suarez to lead the attack alone.
Despite the setback, the Liverpool manager is sure his squad are equipped to go the distance for the rest of the season, although he would still welcome additions when the transfer window opens in the new year.
"Last year, the couple of players we got in January were great and gave us a great boost. It would be brilliant if we could do that again but it's about what's available and affordable," Rodgers said.
"I would love to have that boost because that injection of quality can set you up for the second half of the season. If something comes up to make us better, we will do that, but we do not want to be just adding to the squad.
"It has to be someone who comes in to make us better. If that becomes a possibility, the owners have shown they will support that.
"There is no question we have difficult games. We have two games over the Christmas period against City and Chelsea - the two biggest squads in the league - and that will give them an advantage."
Meanwhile, Chelsea manager Jose Mourinho has accused Romelu Lukaku of being overly talkative with the press and said the Belgian striker needed to explain why he was on loan at Everton rather than fighting for a place at Chelsea.
Lukaku has scored seven goals in eight Premier League games since signing for Everton on transfer deadline day, leading many to question the wisdom of Mourinho in letting him go. With Samuel Eto'o out for at least a fortnight, Mourinho was asked again about Lukaku yesterday, and in particular about an interview the 20-year-old gave to the BBC in which he claimed he had had no contact with Chelsea for "a couple of months".
"Romelu likes to speak," Mourinho said. "He's a young boy who likes to speak. But the only thing he didn't say is why he went to Everton on loan. That's the only thing he never says. And my last contact with him was to tell him exactly that. 'Why do you never say why you are not here?"'
Asked to what he was referring, Mourinho said he would not comment for "ethical reasons" but alluded to an interview Lukaku gave after one of his goals.
"One day he scored and said he 'hoped Jose was watching'? ... like saying 'why did he let me go?' And that's what I'm telling him now: tell the country why you left."
Asked whether he had been happy to let Lukaku go, Mourinho said: "I'm happy that he's scoring goals against our direct rivals and he doesn't score against us, because he can't. But he's there. It's good for his evolution. It's good for Chelsea because he belongs to us for a long time. When you enjoy to speak, speak everything. Don't speak only half of it."