According to the Daily Mail, the fiery pair clashed during a game of head and foot volleyball after Suarez took offence to the defender's imitations.
With pressure building, this could be a sign that the Anfield club are cracking, and it couldn't have come at a worse time with a crucial game against Chelsea on Sunday.
Brendan Rodgers will be keen to stamp out any arguments in the group ahead of their biggest fixture of the season.
A win would put the title tantalisingly close to their grasp, and would require just two more wins to wrap it up.
Both Suarez and Skrtel are known for their fiery temperaments, with Suarez famously biting Branislav Ivanovic last season.
This Melwood melee may be the first sign that there's trouble in paradise, although the Daily Mail reports that a club insider dismissed the incident as boisterousness.
Whilst the players may be beginning to feel the heat, manager Rodgers is portraying a calm exterior.
When asked about the pressure of the title run-in, the former Swansea boss replied: "I'm enjoying being top of the league, It is absolutely wonderful. There is no pressure with it.
"People say, 'You must not sleep at night'. I've never slept better. It's absolutely great, it's why we work.
"I see the joy in the players and in their training - and there is no anxiety. It's good to be involved in. The only way you get the experience is by going through it - win or lose."