Ibrahima Konate was back in Liverpool training on Thursday after a hamstring injury, while fears over other absences can be downplayed.
Konate has not featured for the Reds since the 3-1 win over Bournemouth, and was forced out of France duty over the September break.
But the centre-back stepped up his recovery while on holiday in Paris and was part of the Liverpool squad to return to the AXA Training Centre this week.
A small, 14-man squad of outfielders was pictured taking part in a session at Thursday lunchtime, with Konate involved.
It is likely that the Frenchman will be considered in contention to start for the trip to Wolves on Saturday, then, which comes as a welcome boost.
Trent Alexander-Arnold was not in training despite reporting to Kirkby, as he remains sidelined with the hamstring issue that ruled him out of the England squad.
Konate could come in at centre-back alongside Joel Matip – as Virgil van Dijk is suspended – with Joe Gomez required at right-back.
Also absent on Thursday were the trio of Alexis Mac Allister, Luis Diaz and Darwin Nunez, though there are no concerns over injury at this stage.
Nunez was brought off at half-time in Uruguay’s 2-1 loss to Ecuador as Marcelo Bielsa cited “muscular difficulties,” but it is expected that him, Mac Allister and Diaz are simply due to return later.
That comes after Jurgen Klopp expressed concern over a turnaround of “pretty much 48 hours” for his South American internationals.
Alisson was also on duty with Brazil but should start at Molineux, particularly as he went unused throughout clashes with Bolivia and Peru.
The other two notable absentees were Thiago and Stefan Bajcetic, who were both at the AXA Training Centre but not pictured with the squad.
While there are rumours of interest in Thiago from Trabzonspor ahead of the Turkish transfer window closing on Friday, his absence is not likely to be due to any bid.
More realistic is that he and Bajcetic were following individual programmes after long-term injuries – the latter working in the gym, having played his first minutes since March during the break with Spain U21s.
The majority of those involved in training on Thursday were either not on international duty or based in Europe with their national teams.
Ryan Gravenberch was part of the squad having been given clearance to train with his new team-mates, while Mo Salah made the trip back from Egypt despite having played on Tuesday evening.
Wataru Endo joined training following his involvement with Japan, as their friendlies against Germany and Turkey were held in Europe.
Liverpool squad pictured in training on Thursday
Defenders: Van Dijk*, Konate, Matip, Gomez, Robertson, Tsimikas
Midfielders: Szoboszlai, Jones, Gravenberch, Endo, Elliott
Forwards: Salah, Gakpo, Jota, Doak
* Suspended for Wolves.
