The 24-year-old is contracted to Tinkoff but the team are set to disband at the end of the season due to the fact that no long-term sponsor can be acquired. Team leaders Peter Sagan and Alberto Contador are expected to join Bora and Trek-Segafredo, respectively. Reports in Denmark have indicated that that Valgren is also a major target for Astana.
Alexandre Vinokourov recently told TV2 in Denmark, "Jesper Hansen is a good climber who can help us in the mountains. Valgren can be very important in the classics. I hope we agree with them before the Tour ends."
Team Sky's Dave Brailsford is also an admirer of Valgren, who is currently competing in the Tour de France. The Dane has won a national road title, the Tour of Denmark and earlier this year he finished second in Amstel Gold Race.
Riders are not allowed to announce if they have signed new contracts for 2017 until the UCI's deadline of August 1 but Valgren admitted that contact with Sky had taken place.
"I've talked to them of course but nothing is set yet," Valgren told Cyclingnews at the Tour.
"I've talked to a few teams but that’s a good rumour. I still have to look for the right but I've almost signed a contract so I think I've found the right team already. I can't say anything yet.
"I would love to be on Sky. I think they do it really well and they have riders at the top. I'm still a young rider so I could take a lot of advantage of that. It's very interesting."
Valgren would be the first Dane to sign for Team Sky who have already re-signed Geraint Thomas on a one-year deal.