Mbappe's lawyer told AFP this week the France captain was "shocked" to see his name linked to the investigation and he will take action for libel.
The forward was not selected by France for UEFA Nations League matches after an injury and visited the Swedish capital with a group of people last week.
"In this moment (the reports) are speculations, I see him working every day, he is happy, content, he doesn't seem affected to me at all," said Ancelotti.
"He's looking forward to keep on helping the team."
Ancelotti said Mbappe had been given time off by the Spanish and European champions.
"The days off were set for him and beyond that, individuals can choose what they want to do," explained Ancelotti.
"I don't care where players prefer to rest. I went to London for a couple of days and didn't ask anybody.
"I also don't have a travel agency to organise trips for players."
A Swedish prosecutor has confirmed that an investigation has been opened, without naming Mbappe.
Mbappe claimed in a post on X on Monday there was a link between the report and a hearing before a French league committee on Tuesday over his bitter dispute with his former club Paris Saint-Germain over what he says is 55 million euros (£45.6 million) in unpaid wages.
"FAKE NEWS !!!!. It's becoming so predictable, on the eve of the hearing, as if by chance," he wrote.
Mbappe completed a dream move to join Madrid in the summer after seven years at PSG.
The striker scored five goals in his first seven La Liga appearances before suffering a thigh injury.
Mbappe made a quicker-than-expected recovery but France did not select him for their games against Belgium and Israel, earning the forward criticism in his homeland.
Madrid, three points behind leaders Barcelona, visit Celta Vigo on Saturday with Mbappe expected to start for Los Blancos.
Ancelotti said the superstar attacker looks a "different player" after doing some fitness work during the international break.
"Mbappe took advantage of this break to improve his condition, recover from injuries... he's doing very well, happy and looking forward to playing tomorrow," continued Ancelotti.
"This fortnight has helped him a lot - he's a different player than he was from before the break."