Speculation that Real president Florentino Perez is poised to discard Ancelotti, a year before his three-year contract expires, has been rife since the holders were eliminated from the Champions League and Barcelona secured the La Liga title last weekend.
Ancelotti's post-training news conference on Friday had the air of a farewell, with journalists applauding the Italian at the end, but he insisted he is ready and willing to continue.
Ancelotti led Real to a record-extending 10th European title last term, as well as a King's Cup triumph, and they went on to win the European Super Cup and the Club World Cup before their form tailed off after the turn of the year.
"I understand that this is a key moment for the club because they are taking an important decision," Ancelotti told reporters.
"If I don’t carry on I will have spent two fantastic years here and each will go their separate ways, the club one way and me the other," he added.
"We have had some very happy moments, perhaps the happiest in the history of Real Madrid.
"I won’t be sad as I will have the feeling that I gave everything I could.
"I have the confidence and the desire and the excitement to carry on because I like this club and these players and I like this city."
Spanish media reports have suggested Napoli coach Rafa Benitez, who had a stint working in Real's academy in the mid-1990s, is the front runner to replace Ancelotti.
There has also been speculation that Ancelotti could continue but without his long-term fitness trainer, Giovanni Mauri, and goalkeeping coach Villiam Vecchi, who would be replaced.
Ancelotti dismissed a suggestion a lack of fitness had scuppered Real's trophy chances and defended his assistants.
"I have a lot of confidence in them and they have been working with me for a long time," Ancelotti said.
"What I have achieved in my career I have achieved with this staff and I still think they are the best in the world."
Real are assured of second in La Liga and a Champions League berth for next season.
(Writing by Iain Rogers, editing by Justin Palmer)
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