The 23-year-old, who joined the Reds from Chelsea on Wednesday in a £12m deal, has seen his playing time limited by a hamstring injury this season.
And Rodgers, whose side take on Mansfield in the FA Cup third round on Sunday, says he must be patient before handing the England international his Liverpool debut.
“He’s still catching up on his fitness because he’s been out for a period of time,” Rodgers told a news conference.
“I’m not looking to rush Daniel into anything. He’s looked good in the couple of sessions that he’s had – it’s just going to take a bit of time to get his full fitness.
“That will come through working with the players in the games. He’s not under pressure to come in and perform straight away, in particular because of the level of the team at the moment.
“Certainly over the next few weeks, we can get him up to speed and give him some game time.”
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