Robertson has been absent since the October international break when he dislocated his shoulder while playing for Scotland. The subsequent need for surgery meant an extended period on the sidelines, with the 29-year-old missing 19 Liverpool games so far.
Meanwhile, Robertson's backup, Tsimikas, suffered a broken collarbone during the Reds' Boxing Day draw against Arsenal.
Speaking ahead of Liverpool's Carabao Cup semi-final first leg against Fulham on Wednesday, Lijnders gave positive updates on the two injured stars, revealing that both players could return to team training by the end of January – if all goes to plan.
"Robbo, he's almost at the three-month mark, so he will get checked by the surgeon," Lijnders said, via Liverpoolfc.com.
"And if he does that scan and we see everything [so] that we can really progress him, he will go to Dubai for a week to do proper volume sessions, proper sessions, so that will be good for him. Then we see the three-month-mark scan and then we can see how quick he can go into contact again.
"Same for Kostas. Kostas is progressing really well, really quick. So hopefully both of them – Robbo and Kostas – will be back at the end of this month to train with the team."
The positive update on Robertson and Tsimikas was however offset by news that vice-captain Trent Alexander-Arnold has suffered a knee injury and is set to miss 'a few weeks' of action.
Meanwhile, long-term absentees Thiago Alcantara and Stefan Bajcetic are still some way off a return with Lijnders adding:"They will not be ready for the end of this month. It will probably be going into the next month to train with us. But both [with] no complications, progressing."