The administration-hit club confirmed they had turned down a "second bid from a Championship club" following reports Nottingham Forest had renewed attempts to sign the 20-year-old, who scored three goals in 23 first-team appearances last season.
Hearts fans have allowed the club to rebuff transfer offers after generating more than £750,000 of income since the club went into administration last month, mainly through season ticket sales.
Hearts managing director David Southern told the club's official website: "It's thanks to the fantastic fundraising efforts of the supporters that we are in a position where we do not have to sell our best talent for below market value.
"Gary Locke has a small squad and will face a challenging season so to rid him of another player, and such a talented one as Jason Holt, would not benefit him or the club as a whole."
The deadline for first offers for the club is later today with the Foundation of Hearts supporters alliance the first to submit their offer.