But sources at DIC on Sunday have denied that they have ever "offered the job to Mourinho, or met him to discuss it."
And DIC's representatives, who have good relations with a number of Liverpool fans' groups including the recently formed Spirit of Shankly organisation, have gone to the point on Sunday of contacting them to deny speculation over Mourinho.
Anfield supporters have not forgiven Mourinho for much of the rhetoric and confrontational attitude towards the club taken over the years by the Portuguese coach, particularly involving the Champions League clashes between Liverpool and Chelsea.
So it is being greeted with suspicion that more speculation over Mourinho and Liverpool has surfaced just days before the clubs meet again at Stamford Bridge on Wednesday in the Champions League semi-final second leg.
DIC are acutely aware that if they do eventually take over at Anfield, Benitez has complete backing from the club's fans and any move to dislodge him would be a massive PR blunder.
It is believed DIC have actually been contacted twice by intermediaries for Mourinho suggesting a meeting, but the offer has not been taken up because they are happy with the job Benitez is doing and they are very aware of the reaction from the Kop fans.