Draxler is a win-win situation for us.
One way of looking at him is a great, talented prospect, who isn't happy with his club's current project, and has an extensive highlights reel. He's played on the biggest stages and is very highly regarded. If he comes into the team he'll be useful given the CL games we'll have next year. There's no obligation for him to be integral from day one and we won't be reliant on him, so he could grow into the team without pressure.
Another way is seeing a 23 year old with a consistently shoddy goal contribution, and little improvement from age 19/20. He's flashy but ultimately inconsistent and does not provide any kind of the goals and assist return that a wideman, especially in a Klopp 4-3-3, is expected to provide.
So if we get him, then there's so much upside that it's worth the risk, and if we don't get him, it's not a negative at all. Expecting him to do big things in January is pretty fanciful, so the argument of buying him in Jan to fill in for Mane is redundant. And on the tiny chance that we don't get him and he truly fulfills his potential elsewhere, we can console ourselves with 'he wouldn't fit into our system anyway'.