Assistant head coach Steve Agnew was in charge during their 3-1 defeat against Manchester United on Sunday, with Boro now five points adrift of safety.
The forthcoming worldwide break will give Gibson time to assess the alternatives, but it seems likely that whoever does get the job - Nigel Pearson, Steve McClaren and Alan Pardew feature in the bookmakers' early list of candidates - will have to work within the head-coach model.
Although he has been close to Gibson for years, their conversation following Karanka's exit proved brief.
Boro sacked Karanka on Thursday, with the side 19th in the table having failed to win in the league since December.
Gibson also spoke about the decision to part company with Karanka - but he hailed the Spaniard's achievements during his three-and-a-half-year reign. He sacrificed himself. He's in a good frame of mind. "I think he can be the glue to unify us completely". He has been enormous for our club.
"I hope he's here this time next season, and the season after, and the season after that".
"He's got a wonderful future in football".
Stand-in Middlesbrough boss Steve Agnew says that his team "deserved" a draw from their Premier League clash with Manchester United.
"I've known Steve a long time". We wish him all the very best.
"He is a very good coach, a deep thinker, has loads of experience, knows this club, is a man of integrity and the players trust and like him". Steve could be a surprise No.1. "That may disappoint those people who want glamour and somebody to come in ready-made, a sexy name, but that's not what we need at this point".
Agnew wasted no time in reshaping Middlesbrough's coaching staff in the wake of his temporary promotion, with the hugely experienced Joe Jordan's appointment as assistant head coach confirmed earlier on Friday.
Agnew has now turned to 65-year-old Jordan, who also worked alongside Harry Redknapp at Portsmouth, Tottenham Hotspur and Queen's Park Rangers, to give him some guidance for the challenges ahead.