The German star was heavily linked with a move to Liverpool this season.
But the Reds have pulled out, which has given Chelsea a chance to steal a march in the race.
Now they are set to secure the player, per reports in English, German and Italian media.
And the Evening Standard reports that Man United are not going to make a bid.
They were considering Werner, among other strikers, but their plans have changed.
United secured Odion Ighalo until January, and are happy with their central striking options going into next season.