The box-to-box midfielder is a £3 million target of Boro, who lost Fabio Rochemback at the end of last season.
Reading have already lost Glen Little and Emerse Fae, while John Oster has not been offered a new contract.
Coppell is holding out for more than £3 million for the 27-year-old, due to a clause that states around a third of the sell-on fee must go to Arsenal, but the Reading boss concedes he cannot stop players leaving.
He told the Evening Post: "We don't want to lose players, but I fully accept we are going to because we have players who are desirable.
"You look at Ronaldo at Manchester United – no-one is immune to being vulnerable to so-called perceived bigger and better clubs. We are in a vulnerable position and we have to be flexible."