Owner Roman Abramovich and his key advisers, Eugene Shvidler and Eugene Tenenbaum, visited the training ground on Friday in a visit Chelsea said was routine.
But, coming just a week after news emerged of Cole shooting a student intern with an airgun, a visit by the three most important people at the club was viewed as highlysignificant by insiders.
Best foot forward: Roman Abramovich has ordered a discipline crackdown
Ancelotti is said to have discussed discipline in general and the Cole incident in particular.
Ancelotti's future as manager looks uncertain, with Roma, who are being taken over by American Thomas Di Benedetto, looking to be an option for next season if he leaves Chelsea.
But Ancelotti insists he would prefer to stay at Stamford Bridge, saying: 'I feel good here, I love my club and have another year on my contract.
'One day it is my dream to train Roma because they were my first team as a player. But it's a dream. Not now.
'I expect to still be here the summer after this one. It's impossible to stay here for 24 years like Sir Alex Ferguson has at Manchester United, but more than three years, that is my aim.'
Ancelotti says Tuesday's win over Manchester United shows Chelsea have finally 'woken up', and he has challenged his side to make history by winning Europe's biggest club prize.
'The motivation for the Champions League is fantastic for everyone,' said Ancelotti, who took Chelsea to the Double last season after they went out of Europe to Inter Milan.
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Explore more:People: Alex Ferguson, Roman Abramovich, Carlo Ancelotti Places: Europe