Laudrup is set to make his first move for the Espanyol centre-back, in the hope of completing the deal by the end of this week.
The news comes as a boost to Arsenal boss Arsene Wenger, who is thought to be keen to bring Swansea captain Ashley Williams to the Emirates Stadium.
The report claims Swansea will reluctantly agree to the sale of Williams, but want the transfer sorted sooner rather than later.
The Welsh club are keen to get their squad for the new season finalised as early as possible, and want Arsenal to make their move for Williams before the Premier League season gets underway on August 17.
Arsenal are reportedly unwilling to meet Swansea's £12m asking price for the Wales international, but the deadline could force their hand.
The Swans have lined up Moreno as the man to replace Williams, and feel a deal could be agreed for £7m.
Espanyol are struggling for cash, and Swansea believe a transfer could be completed relatively quickly should Williams leave for the Gunners.
The 25-year-old Mexican defender appeared for his country at the 2010 World Cup.