Sir Alex Ferguson's side are of course chasing an unprecedented five trophies this season and go up against the Italian champions in the knockout stages on Tuesday night.
And Dunn believes Inter's know-how and their manager's nous might just prove too much for a United side that have had things largely their own way in the Premier League of late.
"I think overall it's a huge ask for them (United)," Dunn told the Sunday Supplement. "I actually think the stumbling block will be the Champions League - and more specifically, Inter.
"With Johnny Evans limping off and (Nemanja) Vidic suspended, then for once this impregnable defence looked very vulnerable.
"I just think someone like Inter will have too much. And of course Mourinho has this fantastic record against Fergie, which I think is one (defeat) in 12.
"There's also this slight danger that United have had a fairly trouble-free run recently. There is almost a danger of complacency creeping in; I am sure Fergie will drum it into his side about the task ahead, but I just think there is a danger they'll go into this not having been tested for so long.
"They were tested to an extent yesterday (Saturday) but for so long they've been reeling out this passage of victories and I think this might be a step too far for them."
Dunn also believes that Mourinho - who has made no secret of his desire to return to the Premier League - is the one man capable of tackling Ferguson.
Fellow Sunday Supplement guest Ian McGarry believes the Italians might have too much variation on the field, but it is the battle on the touchline that has taken hold of the News Of The World man's attention.
"We have this idea of huge respect between Fergie and Mourinho but I am sure he must love playing against Fergie ever since the days of Porto and running down the touchline," said Dunn.
"He loves locking horns with him. He's so confident.
"Mourinho will look at that side and I think 'I know how to stop them'. Inter are very strong, very functional and I just think they might have too much for United.
"He has this little bit of a hoodoo over Fergie and although there is this respect between them, I think he fears him Fergie. He is the one manager that has been able to stand nose-to-nose with him."