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.
Laudrup has taken the club to new heights after building on the foundations laid by Brendan Rodgers.
The Swans sit in the top half of the Premier League table and will play in their first major cup final when they face League Two Bradford in the Capital One Cup final at Wembley later this month.
Chairman Huw Jenkins is keen to tie his manager to a longer-term deal and avoid a repeat of the departures of Rodgers and Roberto Martinez before him.
But with that Wembley 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."
But several of Laudrup's players have recently committed their futures to the club, and goalkeeper Gerhard Tremmel became the third this week after agreeing a two-and-a-half-year deal through to 2015.
He joins midfielder Leon Britton and defender Garry Monk in putting pen to paper, and Laudrup said: "It's good to get the players signed up, they are important to us.
"We need to do it quick sometimes because it is difficult to compare and compete with the salaries of other clubs.
"You never know their other possibilities, you have to ask them, but we have to be realistic and know how it is here and the structure is working well.
"We know other clubs pay more money but players sign because they want to stay here which is good for us."