Kouyate's name has also been mentioned with the Hammers resisting overtures to hold on to the trio during the summer as Liverpool repelled Barcelona's interest in Coutinho.
Can is out of contract at the end of the season and is free to discuss moves elsewhere with Juventus looking his most likely destination.
Meanwhile Barca have this week been tipped to renew their interest in Coutinho come January and Klopp has already been forced to fend off fresh speculation, as reported by Sky Sports.
But have the Hammers trio blown any chance of a potential move to Anfield with their woeful form so far this season?
There were signs of improvement in the 2-1 defeat to Manchester City last time out but West Ham realistically need to win eight or nine of their remaining 23 games to have any chance of staying up.
To do that their key trio Obiang, Kouyate and Lanzini will have to start performing. Fail to do so and any hopes of progressing their careers on Merseyside will surely be dashed.