The West London club, who were relegated from the Premier League last season, have reportedly discussed a £15m fee with Albion but are yet to make a formal bid.
Knockaert, 27, has three years remaining on a contract which the French winger signed after his inspired displays in the Championship helped seal Brighton’s promotion to the Premier League in 2017.
He was named the Championship player of the year and scored 15 goals for Chris Hughton’s team.
Scott Parker’s Fulham target an immediate return to the Premier League after a disappointing campaign last season that saw them finish 19th.
Parker clearly sees Knockaert as a player who can add spark to their promotion push and add a further attacking threat, alongside striker Aleksandar Mitrovic.
Brighton could well be open to the idea of receiving £15m for a player they signed for £3m from St Liege in 2016. New manager Graham Potter also has other options on the flanks with new signing Leandro Trossard, Solly March, Jose Izquierdo and Alireza Jahanbakhsh all competing for the wide spots.
Knockaert has also struggled to replicate his fine form from the Championshi. His two seasons with Albion in the Premier League has yielded five goals in 45 starts and 18 as substitute.
Today’s friendly against FC Liefering at the Sportplatz Bischofshofen (1pm) concludes Albion’s week long training camp in Austria.
Potter is expected to give all the players a run-out. “The guys will get 45 minutes and everybody will get that work,” said the new Albion manager. “It will be the end of a nice week hopefully. We have tried to develop the group in terms of team spirit and our own work.”
Brighton will return to the UK and continue their preparations for a third season in the Premier League with friendlies against Crawley, Fulham, Birmingham and Valencia. They kick-off the season on August 10 at Watford.