Holt has been a target all summer for Forest who have had three bids rejected by Hearts administrators BDO, the last of which was £150,000 in July and was described by Jambos boss Gary Locke as "ridiculous".
Reds boss Billy Davies' presence at the Edinburgh derby on Sunday fuelled rumours of another bid from the English Sky Bet Championship club but Hearts said on Monday afternoon that they had received "no fresh bids" for the Scotland Under-21 international.
Hearts entered administration on June 19 and were hit with a transfer embargo and a 15-point penalty ahead of the SPFL Premiership season.
Forest see the Jambos' situation as a chance to get themselves a young, promising player at a cut-price fee.
Since entering administration, Hearts have agreed wage cuts with some senior players while John Sutton left to join Motherwell.
But BDO are adamant any short-term profit made on Holt would only see the club suffer further next season. Fellow Tynecastle youngster Callum Paterson recently backed the club's reluctance to part with Holt, insisting his team-mate has the potential to fetch £10million in the future.
Holt, 20, became a regular in the Hearts first team last season, having made his debut in 2011.
Forest, under Kuwaiti owners the Al Hasawi family, have been flexing their financial muscle this summer with high-profile signings including Gonzalo Jara Reyes, Djamel Abdoun, Jamie Mackie and most recently Kelvin Wilson from Scottish champions Celtic.