The 23-year-old has been heavily linked with a switch to promoted Bournemouth and appears to have resisted moves to tie him down to an extended stay on Teesside.
Manager Wilder told the club’s official website: “We have to get on with it.
“The club did everything to try and keep Marcus. When you get down to the nitty-gritty of the move and him wanting to move, I think it just became a case of negotiating the transfer fee, which is above me.
“But as I say, the club tried everything they could to keep Tav and now we have to look forward.”
Academy graduate Tavernier, whose senior debut for Boro came in an EFL Cup tie against Scunthorpe in August 2017, has made 155 appearances for the club and scored 18 goals.