The United manager was caught on camera as he left the pitch at full-time at Old Trafford, appearing to speak in Portuguese.
Arnold, executive vice-chairman Ed Woodward's right-hand man, interrupted a post-match interview to congratulate the United boss following the dramatic 3-2 win on Saturday evening.
The manager also expressed his disappointment with the board's failure to address what he saw as weaknesses in his squad, particularly at centre-back.
Mourinho, too, has hope and belief that has been absent in recent weeks, even if he claims there is a media "man hunt" against him.
"At half time we were losing 2-0 and the fans were magnificent to the team". We created more chances to score more goals and that's a very positive sign.
"Old Trafford is no longer the fortress it once was. I'm not saying they will start challenging City and Liverpool for the title but it gives them some respite". United return to the Premier League action on 20 October against Chelsea at Stamford Bridge; three days later they host Juventus in the Champions League.
"Maybe it was the wrong decision to play them", said Mourinho.
It was a day where he could be happy with his substitutions though with Mata getting the first and Sanchez getting the victor whilst the decision to move Paul Pogba deeper certainly worked as the Frenchman ran the game in the second half. Sparked by the Stretford End, which had seen all five goals up close, the whole stadium roared, "Oh, United we love you".
But regardless of how stunning the victory was, it doesn't change a thing for United. He spent all summer groaning about a lack of support in the transfer market, then talked about how he had overachieved with last year's squad, one of the most expensive ever put together. They have to be counted and they have to be better.