Everton were quick to reject a joint ?28million bid for the pair last week, on Monday branding it "derisory and insulting".
However, the Toffees statement lacked the 'not for sale' message that has been attached to all official United responses to Wayne Rooney's current uncertain position at Old Trafford.
And for Fellaini in particular, it seems only a matter of time before Moyes gets his man.
"Everton can confirm that it has received bids from Manchester United for two players. Those bids were immediately rejected out of hand as derisory and insulting," said Everton's new director of communications Alan Myers.
"The club did not make public these details as it was vital Roberto Martinez's preparations for the opening game of the Premier League season were not disrupted in anyway."
Moyes stated earlier in the summer that United do need to bolster their central midfield options.
And whilst United's chase for Cesc Fabregas is yet to be abandoned, realistically, with the former Arsenal skipper starting Barcelona's 7-0 rout of Levante on Sunday, the chances of him exiting the Nou Camp this month are remote.
The pursuit of Baines is more puzzling. Patrice Evra has recovered to something like his old form after a difficult 2011-12 campaign.
At 32, he is one of United's most experienced players and was named captain in Nemanja Vidic's absence over the past two seasons.