Yet Sundhage's assertion, made when she announced her squad for this evening's crucial 2015 World Cup qualifier at Fir Park, has been greeted with some bemusement by her Scotland counterpart.
"Flattered, but surprised," would sum up Signeul's reaction ahead of a game which Sweden, especially, cannot afford to lose. Both sides have maximum points in Group 4, but the Scots, who have played one game more than the Swedes, have a better goal difference and would be firm favourites to reach their first World Cup, which is being held in Canada, should they win.
The Swedes have been major players in women's football since they won the first European Championship in 1984; the winning penalty against England was struck by Sundhage. Everything about the way they approach the game, on and off the pitch, justifies their status as the fifth best team in the world, and the third best in Europe.
Signeul, who replaced Vera Pauw as Scotland coach in 2005, was a colleague of Sundhage's in the Swedish coaching system for many years, but their paths first crossed as players. Sundhage, who at 54 is the elder by a year, was a striker and Signeul an opposing midfielder.
"Pia was one of best forwards in the world, and the best in Sweden," Signeul said. "She scored 71 goals at international level."
Both Sundhage and Signeul were among a group of Swedish players hand-picked to be coaches and after obtaining their UEFA A licences worked their way up through the national youth teams. They parted company in 2001 when Sundhage moved to the United States to coach club sides and four years later, having won the European under-18 championship for the Swedes, Signeul moved to Scotland.
While the latter has greatly improved women's football in a country which barely acknowledges her, Sundhage is feted in Sweden and even featured on a postage stamp. After cutting her teeth with Boston Breakers, she later guided the United States to Olympic gold medals in 2008 and 2012.
Once London was over she returned home for the job she always coveted. The ideal script would have seen hosts Sweden win Euro 2013, but they lost 1-0 to Germany in the semi-finals.
"Sweden played some great football in the Euros and the public loved them," said Signeul. "Even when they lost the fans were standing applauding them for 10 minutes after the final whistle - how often does that happen?"
Watching the Swedish players train at Fir Park yesterday, it was impossible not to be struck by their confidence, strength and size. They have the aura of a side which expects to win and which, according to Signeul, have a coach who is among the very best in world football.
This fosters expectation and after training Sundhage was disarmingly candid about the price she would pay if her side does not qualify for next year's World Cup. "If we don't, it's unlikely I will have a job," she conceded, even although her contract runs to 2016.
Like her players, Sundhage is relishing this evening's challenge in Motherwell. "We really respect Scotland's results in the group, but also the way they play," Sundhage said. "Kim Little is a world-class player so we have to painted different scenarios to be able to deal with her."
So what's this about Signeul being her preferred successor? "I was asked the question and I said, absolutely, Anna would be great for Sweden because she has done a fantastic job here," Sundhage added.
n Tonight's match kicks off at 5pm at Fir Park and tickets can be purchased at the gate. It is also live on BBC Alba