The 29-year-old took his goal tally for the season to 21 with a brace in Saturday’s 3-0 win at Bolton and his impressive performances have led to plenty of speculation he could join a bigger club in the summer.
Liverpool, Arsenal and even Manchester City have all been linked with the US star and Dempsey, who has one year left on his current Cottagers deal says he will decide on his future in the summer.
Dempsey said: “We will see what happens. It is one of my best memories of being at Fulham, this season, and I have one more to go.
“I am talking with the club but we will have to see what happens in the summer.
“I want to focus on this season and my football and other stuff can take care of itself after the season.”
Boss Martin Jol has admitted he wants to keep Dempsey but may be powerless to do so if he does not sign a new deal and the club decide to cash in rather than lose him on a free in 12 months time.
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.
Chesterfield boss Jack Lester felt his side were unlucky not to claim all three points after their 1-1 draw at Cheltenham.
New Swindon manager Phil Brown revelled in his side's victory at Cambridge in his first game in charge.