The Italian manager is set to succeed Pep Guardiola at the Allianz Arena in the summer of 2016 for his first role since he was sacked as Real Madrid boss in 2015 following his two-year, Champions League-winning spell in charge.
According to Italian outlet Gazzetta World, Ancelotti is eager to reunite with Bale, Modric and Kroos at Bayern.
The likelihood of all three moving from the Bernabeu to the Bundesliga is minimal, but Ancelotti may be able to persuade one of them to make the switch, especially given Bayern's status in the European game—Bleacher Report's Sam Tighe currently ranks them higher than Real:
Bale would surely be a hugely difficult signing to pull off, even for Ancelotti.
The Welshman is the world's most expensive player and is undoubtedly set to play an even bigger role at the Bernabeu in the coming seasons as Cristiano Ronaldo's career draws to a close—the Portuguese could even depart Real at the end of the current campaign, per Sky Sports' Guillem Balague.
Real president Florentino Perez has previously said that Bale will never leave Real, and given that he is contracted until 2019, a summer departure seems highly unlikely.
Similarly, Modric is seen as "one of the linchpins of the current Real Madrid side," and his intermittent absence from the starting XI has only been because of a desire to keep him fit for the second half of the season, per David G. Medina in Marca.
Kroos, though, could perhaps be tempted by a move back to his former club. (He moved from Bayern to Real in 2014.)
Recent reports have indicated that the 25-year-old central midfielder is unhappy at the Bernabeu, per Frederic Hermel on Spanish TV show El Chiringuito (h/t the Mirror's Ed Malyon).
Per AS, Kroos is seemingly not entirely satisfied with his current role under manager Rafael Benitez:
Should the Spaniard still be in charge in the summer, Kroos may well be tempted to return to the Allianz Arena to play under Ancelotti, who made him a key part of the Real team when the pair were together at the Bernabeu.