Terry, 29, has been in the media spotlight following revelations involving an alleged affair with the ex-girlfriend of Wayne Bridge, the England and former Blues defender who is now at Manchester City.
More details could yet emerge over the following days as Vanessa Perroncel, who is being represented by publicist Max Clifford, considers whether to tell her side of the story.
Controversy: Terry (left) allegedly had an affair with Vanessa Perroncel, the ex-girlfriend of former Chelsea team-mate Wayne Bridge
England skipper Terry has, though, already been given the full backing of Ancelotti and the club, who consider the matter a personal one.
Nevertheless, Sports Minister Gerry Sutcliffe wants talks with the Football Association over the suitability of Terry as captain of the national team.
England manager Fabio Capello is currently in Switzerland recovering from a knee operation, but is scheduled to return later this week.
The FA confirmed on Monday it will be the Italian alone who will decide on Terry's future as England captain.
Born winner: Terry (No 26) leaps to crash Chelsea ahead against Burnley (above), but is unusually subdued in his celebration with his team-mates (below)
Capello is set to attend the Euro 2012 draw in Warsaw on Sunday,which will represent the first public opportunity for him to be pressedon the situation.
England play African Nations Cup winnersEgypt at Wembley on March 3, by which time it is expected Capello willhave made his decision as he looks to maintain a united dressing roomahead of the World Cup.
Terry's ability on the pitch has, though, never been called into question.
The Blues skipper showed no signs of letting the saga impact on his game as he headed in the winning goal against Burnley at Turf Moor on Saturday, even if is celebration was visibly subdued.
Chelsea head to the KC Stadium for tonight's rearranged fixture seeking to extend their lead over Manchester United back up to four points after the champions beat third-placed Arsenal, who travel to Stamford Bridge on Sunday.
Back in the Drog house: Didier Drogba should return for Chelsea following international duty at the Africa Cup of Nations
Ancelotti knows anything other than 100% concentration against the relegation-battling Tigers could prove fatal.
'We have to stay focused against Hull because if we are not, we can have a problem,' the Chelsea boss said. 'We have time after to think about the next game against Arsenal.'
Ancelotti added: 'Every game is difficult here, around the game there is a very good atmosphere and when you play away it is more difficult to win.
'Hull are very able on the long ball, on the head, and we have to pay attention to set-pieces, but we want to do our game.'
Left-back Ashley Cole will have a fitness test on the ankle injury sustained against Burnley, while Ivory Coast striker Didier Drogba is set for a first start since his return from the African Nations Cup.
How John Terry played happy families on theme park day out with wife, his future mistress and Wayne BridgeCHARLES SALE: John Terry lawyer now in Wayne Bridge's team John Terry scandal: It's my call, says Fabio Capello as England boss summons captain for crisis talksJohn Terry backlash - City protest ups pressure on England captain to quitDon't envy the WAGs - I've seen inside their world and it's shallow, lonely and miserableBurnley 1 Chelsea 2: Disgraced Terry keeps on scoring as Chelsea pull clearCHELSEA FC