Before people get all bent out of shape, there's no telling where this story got "leaked" from.
This story could just as easily be coming from the KHL team that owns Willy's rights, because they'd love to grab his attention and get him to at least consider coming to play for their team.
Now if it is coming from Willy's people, then it'd be a definite sign that they're getting desperate and that this whole situation is likely winding down. When Andreas Athanasiou was in his contract dispute with the Red Wings last year, his agents tried playing the "well, maybe I'll go play in the KHL" card too shortly before they ended up caving and signing what Detroit was offering.
The bottom line is, the moment Nylander signs a contract and plays a minute with any KHL team his NHL season this year is effectively over, as he would need to clear waivers before re-joining any NHL lineup this year. So is he really going to write-off this NHL season and his NHL paycheques this year so that he can make a pro-rated two-thirds of a KHL salary (the KHL season is already 1/3 of the way over) and play in some gritty Russian backwater city that's 2300 KM East of Moscow and on the border with Kazahkstan?
I seriously doubt it. Especially since he'd just be in the same position again next year---an RFA with no arbitration rights and no leverage.