Ryan Mason has been conscious and talking to Hull officials after undergoing surgery on a fractured skull.
The former Spurs man was treated on the pitch before being stretchered off and the surgery has appeared to be a success.
A Hull statement read: "The Club can confirm that Ryan has been visited this morning at St Mary's Hospital by club captain Michael Dawson, club doctor Mark Waller, head of medical Rob Price and club secretary Matt Wild.
"Ryan has been speaking of the incident yesterday and will continue to be monitored at the hospital over the coming days where the club will remain in close contact with Ryan, his family and the staff at St Mary's.
"Ryan and his family have also been extremely touched by the overwhelming support they have received and would very much like to thank all of those who have posted such positive comments both on social media and in the press over the last 24 hours."
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It is understood that Chelsea players and staff, including Cahill went to St Mary's Hospital, Paddington, after the game as well.
It is understood Cahill, club captain John Terry and assistant boss Steve Holland spent time with members of Mason's family who had attended the game, which was marred by the incident in the 14th minute.
Both club's medical teams received high praise from brain charity Headway for the way they conducted themselves after Cahill and Mason collided.
Headway chief executive Peter McCabe said: "I was actually at the match and, while it was upsetting to witness the incident, it was encouraging to see the exemplary reaction of the medical teams.
"Headway has been critical of the way in which head injuries have been treated in many high-profile football incidents in recent years, but it is positive to see that lessons appear to have been learned."
Mason received treatment for around nine minutes on the field and later received messages of support from many of his fellow professionals.
Hull issued a statement on Sunday evening, describing Mason's condition as "stable".
The club expect the former Tottenham midfielder to be in hospital "for the next few days".