But even the former Everton manager could be forgiven for asking if someone has had it in for him following his arrival at Old Trafford.
Just two weeks ago, it looked likely that Moyes was about to make a significant impact on the transfer market with the capture of Thiago Alcantara from Barcelona, as Jamie Jackson of The Observer reported.
Despite the disappointing outcome of that pursuit, Moyes remained relaxed as he prepared for his first game in charge in Thailand, as The Independent noted.
Moyes stated in his first press conference as United manager that the United striker was "not for sale," as the Daily Telegraph reported.
However, Rooney left United's preseason tour after just one day due to a hamstring injury, giving the conspiracy theorists an open target to aim at, with Moyes in the crosshairs.
The Scot did little to quash questions over the striker's future when he informed the media on arrival in Australia that Rooney would act as cover for injury to Robin van Persie, as Jackson noted in The Guardian.
In the same article, United chief executive Ed Woodward was also in no mood to be fazed by the question mark over Rooney.
There are no contract renewals that are being discussed. I am not sitting down with any player on an extension and there is no trigger date in the diary. Would we be afraid to run a contract down? Of course not.
The silence from Rooney himself has been deafening. He is reportedly "angry and confused" about Moyes' claim that he was effectively an understudy, as Chris Bascombe of the Daily Telegraph highlighted.
Moyes might have had his problems with Rooney in the past, with his successful libel action in 2008 against the striker, as reported by Caroline Gammell of the Daily Telegraph, often cited since he succeeded Ferguson at Old Trafford.
But the former Everton boss will recognise that, at 27, Rooney is still an impressive member of his squad. That reason alone will ensure Moyes will do all he can to keep the player.
Mourinho, though, is not a figure to sit idly by and wait, and the implicit courting of Rooney will continue until the situation is resolved with United and Moyes.
A 5-1 win over an A-League All-Stars team Saturday allowed Moyes to focus on football, but the nature of the Manchester United job is a far different proposition to his previous 11-year tenure at Goodison Park.
The intensity of the spotlight is now dividing with Moyes openly making his own play for Barcelona midfielder Cesc Fabregas with an improved second bid of £30 million, according to Joe Bernstein of the Daily Mail on Sunday.
With Rooney looking ever likely to link up with Mourinho at Stamford Bridge, the chase for the former Arsenal star could be the defining feature of Moyes' first preseason with United.
Fabregas had appeared to be keen on staying at the La Liga champions, according to the Daily Telegraph, until the sad news of Tito Vilanova's resignation as Barcelona head coach due to illness was announced last week.
With Vilanova leaving his position, the future of Fabregas is unclear but missing out on another Camp Nou midfielder will not be welcomed by United supporters.
But John Richardson of the Sunday Express has reported that another major name may be joining Fabregas in a switch to Old Trafford.
The United manager can dissipate any question marks about his ability to follow Ferguson with at least one of those signatures.
The baptism of fire may soon gain a cooler edge for Moyes.