The Reds look to have received a boost ahead of this week's semi-final encounter.
Can has been sidelined for the Reds' last five matches with ruptured ankle ligaments and had been expected to miss the remainder of the campaign, with his Euro 2016 place thought to be at stake.
However, the report states Can returned to training on Monday and adds that the German is in line to feature in the Europa League semi-final second leg at Anfield.
Can was forced off in the latter stages of Liverpool's 4-3 win against Borussia Dortmund in the previous round and his return will no doubt come as a boost to Reds boss Jurgen Klopp, whose side trail Villarreal by a goal to nil at the half-way stage.
The Sun's report adds that Klopp will hand striker Daniel Sturridge a 'huge show of public support' by playing him from the start against the Spaniards.
Sturridge remained on the bench in Spain last week, despite only two substitutes having been used.