Barnard is currently in the midst of his best ever season appearing in 26 games for Steve Tilson's side and scoring 17 goals.
However, he could be swayed by a bid from the Lions as boss Kenny Jackett seeks to keep the club's play-off push on track.
Ambler revealed Barnard is one of Jackett's transfer targets, although talks have yet to take place with Southend.
He told the Southwark News: "There are a few different targets and the manager has a few different areas he is looking to strengthen if an opportunity comes up," Ambler told the Southwark News. "We are looking at a few different people, but things are still very loose at the moment. Lee Barnard is one of many we've talked about, but I haven't discussed terms with Southend yet."