Villas-Boas press conference
It was suggested by sections of the British media that Cole had confronted Villas-Boas over his strategy after Chelsea slumped to a disappointing last-16 Champions League first leg loss in Naples.
The speculation added to the conjecture over the Portuguese's future, with former Liverpool boss Rafael Benitez this week linked with his position at Stamford Bridge.
Of the reports regarding Cole, Villas-Boas said: "This is not true." He then stressed that he is confident he still has the backing of owner Roman Abramovich: "Yes. Of course."
He did, however, admit that he had to explain his starting XI against Napoli to the club's hierarchy, with the likes of Frank Lampard and Fernando Torres having to settle for a place on the bench.
Villas-Boas said: "I have spoken to the persons near to him (Abramovich). He is disappointed and asking questions about how we set up the team, which were duly explained."