Gervais worked as the manager for Anderson's band Suede before starting his career as a comedian on programmes such as The 11 O'Clock Show and The Office.
Suede frontman Anderson told Shortlist: "Well, he was funny back then. The level of his success has been pretty stellar, but good luck to him - he's a very charming and talented chap.
"He came to a show a few years ago, and it was nice to see him."
Anderson revealed in March that Suede are working on new material, which will be the first studio album since 2002's A New Morning.
Latitude festival will be headlined by the band in July.
Watch the video for Suede's 'Filmstar' below: