The 46-year-old played for Liverpool between 1996-2000 – scoring five times in 48 league games, and now works for BBC Radio Merseyside as a pundit.
The Independent says sources close to the player say he is still confident he will get him move to the Reds.
A fee hasn't been mentioned for his impending switch to Anfield, although it is believed that Mauricio Pellegrino won't listen for offers below £70million.
Thompson said on Twitter: “Vvd on his way to Lfc. Some spending g (sic) going on from FSG."