Cunha took part in the preparations for Thursday's Premier League clash with West Ham United, having missed our two prior games in the competition.
The Brazil forward was ruled out of the home defeat to Everton last month, after picking up a knock in training.
He was also not involved in Sunday's come-from-behind win at Crystal Palace, as Joshua Zirkzee and Mason Mount scored the goals to move the Reds up to seventh.
Ruben Amorim said prior to that contest that he expected 'to have Matheus in the next one', and the boss could provide a further update on his likelihood of featuring in the 20:00 GMT kick-off during his pre-match press conference.