Cleverley was forced out of United's 1-0 win at Everton on Saturday after experiencing discomfort in his ankle and was not among the 25 players who trained at Carrington.
Ashley Young, Ryan Giggs, Federica Macheda and Chris Smalling were also missing, while midfielder Michael Carrick trained on his own.
Skipper Nemanja Vidic was part of the main group, although the Serbian will not feature on Wednesday as he is suspended following his red card in Bucharest a fortnight ago.
Most interest surrounded the presence of young trio Paul Pogba, Larnell Cole and Ezekiel Fryers, although whether any of them will be involved remains to be seen.
United are currently second in Group C and will expect to record a comfortable win against opponents who appeared limited in Romania, thereby enhancing their chances of reaching the knockout phase.