The Danish manager's agent, Bayram Tutumlu, said on Wednesday Laudrup is set to begin contract discussions with the Welsh club's board "in the coming days".
The 48-year-old boss has enjoyed an impressive debut season in South Wales so far, guiding the Swans to the Capital One Cup final as well as keeping them in the top half of the Premier League to build on last year's maiden top-flight campaign under Brendan Rodgers.
Laudrup, who succeeded Rodgers in June, is out of contract at the Liberty Stadium next summer.
But reports suggest the Dane is likely to be offered a 12-month extension and the manager is keen to stay on.
He told The Sun: "I have said more than once my intention is to stay. We are way ahead of what I could have imagined - being in a league cup final."