Lambert closer to Reds switch
The Anfield club are understood to have agreed a £4million deal for the 32-year-old, who was once on their books as an academy player.
Lambert told Sky Sports News: "The medical went well but as you know I can't say anything.
"I'll speak properly about it, hopefully, very shortly.
"It's been a crazy football year to be honest, the way it's carrying on."
Lambert was asked if he had spoken to Liverpool captain Steven Gerrard about the move while with him on England duty over the past week.
He said: "I've spoken to Stevie a while ago, but I'll speak properly on Monday."
News of Lambert's impending move to his boyhood club came as a surprise when it emerged on Thursday evening.
Lambert was released by Liverpool at the age of 15 in 1997 and was later shown the door by Blackpool after moving to the Lancashire club as a trainee.
Having helped Saints to two promotions and then impressing in the Premier League, he admits he will leave St Mary's with a heavy heart.
He said: "There's lots of emotions as you can imagine so it's something I need to address and obviously I will address all parties when I get the chance."
Liverpool are also understood to have made an improved offer of £25million for Lambert's Southampton team-mate Adam Lallana after having an initial £20million bid rejected.