The Whites owner is not happy with the 22-year-old or his agent, who also represents ex-Elland Road defender Sam Byram.
Taylor, who is attracting interest from Premier League pair Burnley and Middlesbrough as well as Championship rivals Newcastle United (Guardian), recently entered the final year of his contract at Elland Road.
Despite being one of Leeds' standout performers over the past two campaigns, the club are yet to tie down the 22-year-old to a long-term contract.
And, according to Cellino, it's through no fault of his own.
"I'm very disappointed with the way he has acted," the Italian told the Daily Mirror. "We are not going to let him go. Trust me!
"For almost one year, I've been trying to get him to sign a new contract."
Cellino's beef is not only with Taylor, but has agent Colin Pomford - with whom he has previous.
He added: "The agent is the same as Sam Byram's (who Leeds sold to West Ham United with six months left on his deal). But I promise, even if we lose him at the end of the season for free, I'm not selling him."
Even if Taylor was to run down the final year of his contract, his age keeps Leeds protected, in theory - provided they offer him a new one on equal or greater terms.
Any English club who signs the York-born star would still have to agree terms with the Whites, otherwise a tribunal hearing would be required to determine the fee.