The 24-year-old this week moved to reassure O'Neill that he was happy on Wearside after agent Guy Vandermissen hinted he may have to leave for a higher-profile club if he is to achieve his ambition of replacing Thibaut Courtois as Belgium's first-choice goalkeeper.
O'Neill, who celebrates his 61st birthday on Friday, revealed talks over an extension at the Stadium of Light are under way despite Mignolet having two years of his existing deal still to run, and the Northern Irishman is determined to resolve that situation as quickly as possible.
He said: "We would really like to try to tie him down to a longer contract. There have been talks about that for some time, but I think we would really want to try to firm that up as soon as we could. I think he's receptive to it."
Mignolet has arguably been Sunderland's best player in a testing Barclays Premier League campaign to date, and the fact that he acted swiftly to silence the alarm bells will have come as a relief to O'Neill and the club's supporters alike, although the former was relaxed about the whole situation.
He said: "I hadn't been made aware of it at all and he came up to me to tell me that he thought there was something lost in translation.
"The agent who was working in the office had made some comment about it and really, if you think about what he said - I haven't seen it first hand and therefore, it's unfair of me to make a comment - but if the gist of it was that Atletico Madrid are a better side than Sunderland, well I am not so sure that too many people would disagree with that.
"I haven't a major problem with that. Our job is to try to make us at some time or another as good as them."
Mignolet will hope to underline his importance to the Black Cats once again on Saturday as he and his team-mates attempt to end a run of three successive league defeats by beating Fulham at the Stadium of Light.
They will do so with Republic of Ireland winger James McClean once again having been told to let his football do the talking.
The Derry-born 23-year-old this week closed his Twitter account in the wake of criticism over a tweet about the Wolfe Tones song the Broad Black Brimmer, which tells the story of a boy whose father is killed fighting for the IRA.
O'Neill said: "James himself came off Twitter before I had the conversation with him anyway, and I think he realises now. He wants to really concentrate on the game.
"He felt he was, (talking to McClean) but come off this and go and get yourself back to where you were, playing brilliantly for us this time last year."
O'Neill will be without skipper Lee Cattermole, who is facing several weeks on the sidelines after having an injection in his injured knee in a bid to avoid surgery, and hamstring victim Danny Rose.
Meanwhile, the manager has expressed his delight at Sunderland's new partnership with the Nelson Mandela Foundation.
Asked how the link with the former president of South Africa compared to the big names with whom he has worked over the years, O'Neill replied with a smile: "None bigger than him, honestly.
"He said that if McClean didn't improve his performances, he was coming to play outside-left for us.
"It's really big, I must admit. He's up there with Kennedy and Martin Luther King, so there we go, it's really big. We pull them in, don't we?
"It's massive. Seriously, it's incredible. I wasn't aware of that until quite recently. It is really something.
"We should get him over for a couple of games. Maybe he will give us his blessing and push us up the table."