Livermore is a left-sided midfielder but can play in central defence and also at left-back. He has made more than 300 appearances for the South London club, scoring 14 goals.
Livermore handed in a transfer request at the end of last season and Millwall have decided to accept an offer believed to be in the region of £400k.
The former Arsenal trainee, who also asked to leave last season, has been at The Den since 1999 and played in the FA Cup final, as well as helping the Lions to promotion in 2001.
Millwall boss Nigel Spackman recently admitted he had received a bid when he said: "We have received an offer for one of my players and we will look at that.
"Naturally if another club makes a serious offer for one of our players then we need to consider it, but I have to know that I can find quality replacements which isn`t always easy."