But Liberty Stadium insiders say they are not expecting any bid, citing the agreement between Rodgers and Swans chairman Huw Jenkins struck when the former left South Wales for Merseyside.
Rodgers himself admitted that meant he could not instigate a bid for any Swansea player for 12 months - unless they became available on the market.
And the Danish legend admitted he was delighted with how his first foray into the transfer market had gone after the arrivals of defender Chico from Genoa and attacking midfielder Jonathan de Guzman from Villareal.
Laudrup insisted he will hope to add further new faces to his squad, but outlined the importance of fitting in to Swansea's familiar style of ply.
"I'm very pleased to get two players in, two that I wanted and who I know," said Laudrup after shelling out £2.5m for Spanish centre-back Chico before landing Dutchman de Guzman on a season-long loan.
"Chico is Spanish but he could have been born here because he has that aggression to his game and he is very good in one against ones.
"And Jonathan is someone who will fit perfectly into the way we play here from the midfield. It's important that players come in adapt to the style of the team and I know both of these will do that 100% and very quickly too.
"There are a couple of players I'd still like to come in but it was important I came in to have a look first and give people a chance."