Matip has been strongly linked with a move to Liverpool, but in the summer.
The Reds the possible situation of having no senior central defenders available for Friday's FA Cup third round tie against Exeter City with Dejan Lovren picking up a hamstring injury in Tuesday night's League Cup win over Stoke City, and Kolo Toure was also seen limping after the final whistle.
Mamadou Sakho missed the game due to a knee problem while Martin Skrtel is sidelined until the end of the month at least because of a hamstring injury of his own.
Liverpool's interest in Matip has been well-known, and his contract at Schalke runs out at the end of the season, meaning he will be available on a free transfer.
Klopp is said to prefer signing the player in the summer on a Bosman ahead of next season.
Some will be wondering why Liverpool don't pay whatever fee it takes to try and get the defender over to Merseyside now, given that he is a player that Klopp is clearly keen on and it won't be a matter of signing a quick fix.
In his post match press conference following the game at the Britannia Stadium, as reported by the Liverpool Echo, Klopp suggested that he will be looking to strengthen in defensive areas following the recent spate of injuries.