The 41-year-old has been in charge of the Denmark Under-21 side, but is to give up the role to move to the Liberty Stadium, and his switch could be confirmed before the weekend.
Erik Larsen has been working as Laudrup's right-hand man so far this season, but it is believed he will be moved into a position with more focus on scouting, while Alan Curtis will remain as a first-team coach.
During his time in Glasgow Wieghorst helped Celtic end Rangers' run of nine-straight SPL titles, before being diagnosed with Guillain-Barre syndrome in 2000 and making a remarkable return to resume his playing career.
Wieghorst, who played alongside Laudrup for Denmark, left the Hoops in 2002 to become one of his former team-mate's first signings at Brondby. The highlights of his managerial career to date have been the consecutive Danish Cup triumphs he oversaw with Nordsjaelland, before taking the reins of the national under-21 side.
He was also viewed as a potential successor to Morten Olsen, with the boss of the senior Denmark side set to step down next year, but the chance to return to club football has been too strong a draw.
The move to bring in Wieghorst would suggest Laudrup has no intention of leaving the Liberty Stadium, having been linked with Real Madrid and Chelsea. Despite the speculation, the Swans boss does not believe there is any need to rush a decision over extending his contract, which runs out at the end of next season.
But with a Capital One Cup final, important Premier League games and next week's warm-weather training camp in Dubai on the horizon, Laudrup does not believe his contract is a matter that needs to be dealt with immediately.
He said: "I think for me the present is more important than the future, we have so many things coming up now and I already have a contract for next season so it is not urgent for me.
"We have some very important things to deal with right now. I am talking to the chairman a lot of times every week and we talk about a lot of things."