It has been suggested for weeks now that United believe they can lure Ronaldo back to Old Trafford, where he left in 2009 for Real Madrid in a world record £80million deal.
And a report in Spanish paper El Pais today claimed a meeting would be taking place between United officials and Ronaldo "in the next few days" to see if there is any likelihood of a transfer being completed.
United have not commented on the report, although it is obvious a deal would be hugely complicated given apparent interest from Paris St Germain and supposed advice given to the former world player of the year to remain at Real Madrid for the final year of his contract.
New Madrid coach Carlo Ancelotti presumably would prefer to keep Ronaldo as he begins the task of shaping the club following Jose Mourinho's exit.
However, Ancelotti is unlikely to have the final say if Ronaldo decides he wants to leave.
It merely adds to the air of uncertainty at United, with Moyes set to officially begin work on Monday, with his squad due to begin training later that week.
Chief concern will be to work out the best way forward for Wayne Rooney who, like Ronaldo, has been the subject of some much, often conflicting, speculation.
PSG, Bayern Munich, Chelsea and Arsenal have all been linked with the England forward at times this summer, whilst it has also been stated Moyes would prefer to keep the player he introduced to senior football whilst at Everton.
If that is Moyes' wish, it is unlikely to be fulfilled without some sort of clarification on the supposed transfer request Sir Alex Ferguson claimed Rooney had made at the end of last season.
It has now been established Rooney did not express any such desire, merely sought clarification about his status with Ferguson.
Yet any public statement to that effect by United would undermine the man who brought them 13 Premier League titles and left at the end of the season with his status as an all-time great beyond question.
The side issue involving Rooney is that both Shinji Kagawa and Danny Welbeck spent much of last term operating out of position, whilst Javier Hernandez's first-team opportunities were also restricted.
If Rooney stays, at least one of that trio is bound to wonder whether they have any long-term future at United.
At least the picture won't be made even more complicated by the arrival of Edinson Cavani as United have privately distanced themselves from reports of an interest in the Napoli front-man.