The former Tottenham midfielder was expected to join the Clarets and has held talks with officials at Turf Moor about a £1m move.
But the deal has been put on hold after manager Brian Laws went on holiday.
The Tigers were hoping Marney would be the first player to be sold as they look to reduce a wage bill of £38m.
But Marney has been left in limbo and Forest boss Billy Davies could now step in and offer him a move to the City Ground instead.
Laws said: "There's no truth in the rumour that we've offered £1m. Nothing has been done or said yet. All we have done is make enquiries about him and spoken to the club.
"He's one of a number of players we're interested in. We're just looking around."