He joined Liverpool in a potential £34 million deal this week.
The 24-year-old attacker joined Liverpool from Southampton for up to £34 million on Tuesday afternoon to become the Reds' first major signing this summer.
The jet-heeled Senegalese forward netted 24 times during his two years with Southampton, making him an obvious goal threat in Jurgen Klopp's side.
Although Thompson has acknowledged that Klopp needed a player of Mane's ilk, the Sky Sports pundit feels that the German paid "far too much" to get him.
"I see it as an absolutely pivotal signing, one that was needed as the other attacking midfielders are more technical players and don't really have the pace," said Thompson.
"Philippe Coutinho, Adam Lallana and Roberto Firmino are all quite similar so I'm not surprised Klopp has looked to add something different - a player that gives them a threat on the counter-attack and also adds goals.
"Daniel Sturridge also seems to have lost his pace a bit, probably due to the amount of injuries, which we saw with Michael Owen, so there's only really Divock Origi who can stretch teams."
"I think we've paid far too much for him," Thompson added.
The former Red Bull Salzburg man is indeed pricey, but he is proven in the Premier League and he is only going to improve under a man-manager of Klopp's vintage.
Liverpool fans will have seen first hand how devastating he is, having netted two good goals against the Merseyside outfit in a 3-2 Southampton win back in March.
One question mark over him is perhaps whether he can score goals at a consistent rate by Liverpool standards, but time will tell.