Steve Cooper's side have been busy during the summer transfer window so far, as the Reds boss continues to revamp his squad ahead of their long-awaited return to the top flight.
Seven additions have already arrived through the door at the City Ground since the end of last season, including the likes of Dean Henderson, Neco Williams, Omar Richards, Moussa Niakhate and Taiwo Awoniyi.
However, Forest are not done with their business just yet, as the Daily Mail are reporting that Tavernier is the latest to be the subject of interest from the newly-promoted side.
The report suggests that a £10m offer has been tabled, which matches the offer currently in place from Bournemouth as well, who also achieved promotion from the Championship last season.
Both clubs are awaiting an answer from Middlesbrough as things stand, according to the report, with it not yet clear what their stance is when it comes to the midfielder's future.
Tavernier scored five goals and registered as many assists across 44 league appearances for Boro last season, helping his side to overcome a poor start by narrowly missing out on a playoff place.
The academy product is the latest midfield target for Forest, with Cooper keen to bring in reinforcements in the centre of the pitch following the end of James Garner's loan spell, as well as it being identified as an area requiring improvement ahead of the new season.