Brendan Rodgers swapped the Liberty Stadium for Anfield in May following the sacking of Kenny Dalglish, and the Northern Irishman is keen to make Allen his second Liverpool signing.
The Reds have already had a £12.5m offer rebuffed by Swansea, and Laudrup insisted the Team GB star merits a big transfer fee by virtue of his impressive performances last season.
“He is worth a lot of money because he’s a good player,” said Laudrup.
“The manager knows him and knows if he wants to change the way Liverpool play he needs a player in the midfield like Joe Allen. But he also knows he’s very, very expensive.”
The former Denmark international also referenced Liverpool’s extravagant purchases of Alberto Aquilani (£17m), Jordan Henderson (£20m) and Stewart Downing (£20m) over the past three seasons.
“We saw they bought a couple of midfielders in the last few years for a lot of money, but with all due respect Joe is on a level above,” he added.
“In my opinion, if one is worth £17m then Joe is worth more, perhaps over £20m. I’m talking as a football man not as a chairman but if the chairman asks my advice then I will tell him the same.”
Laudrup was announced as Rodgers’ successor at Swansea in June, and the former Getafe manager has already signed José Manuel Flores, Michu and Jonathan De Guzman.
The Swansea manager is happy with his current squad and the 48-year-old is not interested in bringing any of Liverpool’s fringe players to the club as part of a potential deal for Allen.
“If we could have [Luis] Suárez,” he said when asked about the possibility of an exchange. “We have good players here and they have good players, but I can’t see a player not in the starting 11 at Liverpool being in the starting 11 in our team.
“They might want to do it because they can pay less money.”
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