Clint Dempsey has missed Fulham's pre-season tour of Switzerland so he can "work on his fitness".
The United States international has been linked with a move to Liverpool, who confirmed last month they are interested in signing the attacking midfielder.
Fulham spokeswoman Katie Holmes said Dempsey has remained in London "to work on his fitness" with the youth team and refused to comment on media reports concerning a possible switch to Merseyside.
It has been reported that Dempsey and Fulham manager Martin Jol were involved in a fiery debate before the squad flew out of London.
Liverpool manager Brendan Rodgers told his own club's website in July: "Clint is a player we've enquired about, it is as simple as that.
"Ian Ayre, our managing director, has spoken with the club (Fulham) to see what the position is. That is where we're at.
"He's a very talented player but we don't like to talk about other clubs' players."
The 29-year-old scored 23 goals in 46 games for the Cottagers last season.