Tudgay is out of contract at Forest next month and he could leave the club on a free transfer.
However, Forest boss Billy Davies is a big fan of Tudgay and is keen to keep hold of the striker by offering him a new one-year contract.
Tudgay enjoyed a successful two-month loan spell at Barnsley last season, scoring three goals in nine appearances before returning to Forest and featuring in two games at the back end of the Championship campaign.
The striker's agent, Darryl Powell of Paramount Sports Management, has confirmed Tudgay is weighing up Forest's contract offer.
"Forest have offered Marcus a new one-year deal and he is weighing up all his options," Powell told Sky Sports.
"Marcus loves it at Forest and playing under Billy Davies even though he would have liked a bit more security with a longer-term contract offer."