I doubt klopp ever said that. Anyways, it's not impossible but we'd have to pay aroud what we paid for di maria to bring in hummels. And that's just to get Dortmund to say yes. After that it'd be up to Hummels, and I doubt he'd want to leave dortmund for United at this point.
Also, dortmund don't really sell their best players. Whenever they leave its not through their choice. They rejected like 35m for lewandowski last year because they would rather make him leave on a free then cash in. Gotze had a release clause. Reus has a release clause which will let him leave. Sahin had a release clause. Kagawa had a year left on his contract and klopp lined up reus anyways. They're just in a much better situation financially now then before, and though they aren't as big of a club financially and can't offer wages like United, they are still a huge club and currently a better one then United.