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.
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.
Alisson was also on duty with Brazil but should start at Molineux, particularly as he went unused throughout clashes with Bolivia and Peru.
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.
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.