The Reds take on Inter in the second leg at Anfield on Tuesday night, with Jurgen Klopp putting his squad through their paces in an early evening session.
However, Konate was absent after an intense game against West Ham at the weekend, with the Frenchman likely in second-day recovery following his 15th start of the campaign.
Rhys Williams, the 21-year-old who returned from an unsuccessful loan at Swansea mid-season, was part of the session, though, having been registered as part of List B in Liverpool’s Champions League squad.
It is unlikely Williams will be involved on matchday, despite Klopp being able to name 12 players on his bench, with the youngster effectively fifth choice this term.
Liverpool hold a strong 2-0 lead heading into the second leg, though the manager was eager to stress that it remains a dangerous result to rest on.
“If you’re at half-time being 2-0 up and you have a team who thinks ‘we are halfway through’, you are already on the wrong path,” he told reporters on Monday.
“We are long enough in this, we know that. It’s a much better result than I would have expected, to be honest, before we played there.
“The game didn’t look like we would win it 2-0 for most of the time, it was a really tough tie and a really difficult game to play.
“We knew before they had quality; after, we know they have real quality. So now they will show up here.”
Liverpool squad in pre-Inter training
Defenders: Van Dijk, Matip, Gomez, R.Williams, Alexander-Arnold, Robertson, Tsimikas
Forwards: Salah, Mane, Jota, Firmino, Diaz, Minamino, Origi