The Cottagers have opened talks with the veteran pair, who are currently in the last year of their contracts.
Duff has proved a hit since joining from Newcastle in 2009, with the 34-year-old winger signing a contract extension in February to keep him at the club until of the summer of 2014.
Jol wants the experienced star to stay on if his fitness allows, telling the Sunday People: "Damien is a true professional and we will give him an extension if he can play for another year."
Midfielder Sidwell has established himself as a key player since arriving from Aston Villa in January 2011 and Jol had already revealed the club has opened talks.
He re-iterated the club's desire to keep hold of the 30-year-old, saying: "We want to keep our best players. We are talking to Steve about extending and we think he wants to stay here for longer."