The Dutch boss spoke candidly and openly at a question and answer session at a Fulham Business Club event last night.
Jol is aware that Dempsey is interesting several top clubs as he prepares to enter the final 12 months of his Craven Cottage contract, but the Fulham boss is still hoping to convince his top-scorer to stay at the club.
Fulham have put a two-year extension on the table but the 29-year-old American admitted in January that he wants to play Champions League football.
However, Jol will not let the matter drift when the season comes to an end next month and stated that he will be looking to offload Dempsey quickly once the transfer market re-opens if the forward has not put pen to paper by then.
Dembele, who Jol knew from his time in Dutch football as Ajax coach before he took over last summer, has also been linked with a move away after another highly-promising season.
The Fulham boss compared the Belgian to Spurs’ Rafael van der Vaart earlier this season and told fans that he rates Dembele as worth £15m in the current transfer market climate.
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.