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.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.