The 29-year-old admitted this week that he wants to play in the Champions League after an eye-catching season at Craven Cottage that saw him score 17 goals in 37 appearances for the west Londoners.
"If he has the opportunity to go to a Champions League team, that's the crème de la crème of club soccer then you have to do that" - Jurgen Klinsmann
And national team boss Klinsmann believes the time is right for him to move on.
"If you play consistently at the highest level then offers will come in. I think everybody is aware of that. His goal is the right goal, we have often discussed it," he told reporters.
"If he has the opportunity to go to a Champions League team, that's the crème de la crème of club soccer then you have to do that, with all the respect obviously to Fulham, as he often mentions.
"But you want to play in the biggest club competition in the world and that's the European Champions League and hopefully something will happen over the next couple of weeks.
"If it doesn't happen then he has to keep pounding away and knocking at the door."
Dempsey has been ruled out of USA’s clash with Scotland on Saturday with a groin injury but hopes to return in time for their meeting with Brazil four days later.
Klinsmann revealed they have yet to discuss the former New England Revolution star’s future since linking up for training this week but admitted he has been in regular contact this season.
"We haven't talked about it yet [this week] - but before on the phone, following up his Premier League games we discussed different ways of approaching things," said the German boss.