Vydra joined Watford on a permanent basis in the summer from Udinese after two separate spells at Vicarage Road.
In between his two loan stints at Vicarage Road, Vydra spent the 2013-14 campaign in the Premier League with West Brom, scoring three goals from 25 appearances.
The Czech Republic international played a key role in Watford's promotion to the Premier League last season, scoring 16 goals as Watford finished second in the Championship.
Vydra has been an unused substitute in Watford's opening two Premier League games against Everton and West Brom with new boss Quique Sanchez Flores preferring Troy Deeney and Odion Ighalo in attack.
A number of clubs are thought to have made enquiries about taking Vydra on loan if he is not going to be a regular for Watford this season.
Forest, who are only able to make loan signings or bring in free agents, are thought to be at the front of the queue to try and sign Vydra on loan as they look to bolster their attacking options.