Fulham showed they hardly needed last season's top scorer when they romped to a 5-0 home win over Norwich City on the Premier League's opening day but Jol's post-match news conference was still dominated by Dempsey's no-show.
"If you want to move you don't want to take risks, you don't want to play because you could get an injury. That's a very awkward situation for us and for me and for him as well," Jol told reporters.
"Maybe Clint knows more than us but we feel and the players feel and everyone else feels that he should stay here if there is no other bid because there is no other bid.
"In a normal world you have to stay where you are because you signed your contract and hopefully he will play for us again." added Jol.
Arsene Wenger's Arsenal side, who drew 0-0 with Sunderland, are in Europe's elite competition and need fresh forwards after selling leading striker Robin van Persie to Manchester United.
