The Whites are believed to be rivalling Wolves, Sheffield United and Derby for the 18-year-old’s signature.
Football's top transfers from the 2019 summer transfer window so far
McCarron, who signed a new 18-month deal with the option of a further year last September, made 20 appearances in a breakthrough season for Carlisle in League Two.
The Daily Mail report Leeds boss Marcelo Bielsa is keen to bring the midfielder to Elland Road before the start of pre-season.
Leeds are understood to be leading Premier League duo Wolves and Sheffield United in the race to sign McCarron due to the likelihood of guaranteeing more playing time in the Championship.
Last week, Carlisle director of football David Holdsworth confirmed there is interest in McCarron from various clubs.
He said: “We have received interest from a number of parties regarding both Jarrad Branthwaite and Liam McCarron.”