The PFA Players' Player of the Year was notably absent from the team portion of the session at Melwood, though a club spokesperson has claimed he, Alex Oxlade-Chamberlain and Adam Lallana took part in individual sessions, though only the latter will definitely miss Tuesday's clash at Anfield.
Reports suggested Oxlade-Chamberlain may have sustained an injury while warming up on Sunday against Newcaste, a match in which he made the bench but did not feature.
However, no specific reason was given for either his or Van Dijk's absence from the team session.
Facing a 3-0 deficit after their first-leg defeat at Camp Nou on Wednesday, Liverpool already face the unenviable task of attempting to rally at Anfield without at least two of their stars.
Roberto Firmino will miss the clash with a muscle injury after only being fit for a cameo appearance in the first leg, while Mohamed Salah will also be absent as he recovers from a concussion sustained in Liverpool's dramatic 3-2 victory over Newcastle on Saturday.
Salah collided with Newcastle goalkeeper Martin Dubravka and was down for several minutes before being stretchered off for Divock Origi in the 73rd minute.
It was Origi who netted the winner 13 minutes later, as his header from a Xherdan Shaqiri free-kick deflected in off Newcastle defender Jamaal Lascelles.
Van Dijk, who scored Liverpool's opener in the victory, proved instrumental in the sequence, as he directed Shaqiri to take an in-swinging free kick over Trent Alexander-Arnold.
The towering centre-back has been a lynchpin in a Liverpool defence this season which has conceded only 22 times this term, the joint-fewest goals in the Premier League with Manchester City.
Liverpool require at least a matching 3-0 victory over Barcelona to force extra-time on Tuesday and should they concede even once, need a win of four goals or greater to advance to the final against Tottenham or Ajax.
In addition to question over the Barcelona clash, there may be concern toward the Premier League finale on Sunday against Wolves.
Liverpool could win their first Premier League title with a victory in that clash, provided City drop points in either of their final two matches of the season against Leciester or away to Brighton in the league finale on Sunday.