Mohamed Salah and Virgil van Dijk are expected to be available for selection for Liverpool's trip to Huddersfield Town on Saturday, while Naby Keita looks to be sidelined for around two weeks, sources have told ESPN FC.
Salah and Van Dijk withdrew from their national teams over the international break amid fitness concerns, but trained at Melwood on Thursday afternoon.
A source close to Keita in Guinea told ESPN FC that the player is expected to be ruled out for at least two weeks with his hamstring injury.
Sadio Mane's availability remains uncertain after he had surgery on the fractured thumb he suffered when away with Senegal and was absent from full Liverpool training on Thursday.
Salah was forced off late in Egypt's Africa Cup of Nations qualifier with Swaziland on Saturday because of a groin issue and missed the return fixture three days later.
Van Dijk, meanwhile, has been battling broken ribs for several weeks, according to Netherlands boss Ronald Koeman, and sat out Tuesday's friendly with Belgium.
James Milner also trained on Thursday, having injured his hamstring in Liverpool's game with Manchester City over the international break.
Salah and Van Dijk returned to Melwood, where their fitness was assessed by the club's medical staff, and look set to be fit to feature against Huddersfield, who sit 18th in the Premier League table.
While Jurgen Klopp is expected to be able to call upon two of his most important players on the weekend, he is set to be without Keita for a short period.
Keita sustained the issue while playing on an artificial surface for Guinea in Rwanda on Tuesday.
Huddersfield boss David Wagner, however, believes Klopp, an extremely close friend of his and teammate at Mainz in their playing days, may be overplaying Liverpool's injury problems.
"I have known Jurgen long enough, I know he loves to use smokescreens," Wagner told a news conference on Thursday. "I expect that most of his players will be available.
"I have known him long enough and he likes to moan after the international break."
Liverpool have made a strong start to the campaign with 20 points from eight matches to sit third in the table as one of three unbeaten sides.
Huddersfield's form is a stark contrast as they seek a first win to potentially climb out of the relegation zone.
Wagner said Saturday's match represented a chance to build on a 1-1 draw at Burnley last time out.
"Now we have a great opportunity, a wonderful game in front of our fans against a very strong side, where we can hopefully perform at the same level [as our last game]. That's what we like to do," Wagner added.
"Every performance gives you belief and every win gives you belief -- unfortunately we have no wins so far -- but we have performed at a good level consistently over the last weeks and in training the guys look very good as well.
"Sometimes football writes some great stories and nobody knows what is going to happen on Saturday."
Information from Reuters was used in this story.