Former Arsenal midfielder Lansbury, 26, is out of contract at the City Ground in the summer.
Lansbury has scored six goals in 19 appearances this season, including a hat-trick in a 5-2 win over Barnsley.
The Londoner has not played since picking up a hamstring injury before the 3-0 loss at Derby on 11 December.
Lansbury has previously been the subject of intense transfer interest, with Burnley in contact with Forest about a deal for the player in August 2015, but Lansbury decided to remain with the East Midlands club.
The Reds have started 2017 under a transfer embargo because there has been a delay in submitting audited accounts as the takeover of the two-time former European Cup winners nears completion.
Nottingham Forest have rejected Derby County's offer of more than £2.5m for captain Henry Lansbury, reports BBC Radio Nottingham.