The Irishman is one of several names on the club’s radar as they search for a replacement for Besnik Hasi, who was sacked yesterday.
It was that setback, the second in two seasons following Gent’s success in 2014-15, which prompted Anderlecht to fire Hasi after just over two years in the post.
Veteran Olsen, 66, would be favourite with the fans because of his special status as a player in the Anderlecht side which won the UEFA Cup in 1982.
At 44-years-old, Lennon is the youngest candidate, but has Champions League experience with the Hoops. Anderlecht will also have to pre-qualify this summer, going in at the third qualifying round, with Brugge taking the only group stage passport.
Two days ago, Lennon revealed he had been close to rejoining Celtic but lost out Brendan Rodgers. However, he admitted he also saw a future abroad after the torrid time at debt-ridden Bolton, who were relegated to the English third tier at the end of the campaign.