According to the British media, Liverpool have been told to increase their offer for the uncapped Brazilian playmaker after initially offering a reported £24.6m for Teixeira.
Former Manchester United striker Javier Hernandez and Udinese midfielder Piotr Zielinski are also touted as Liverpool targets for Klopp.
Speaking at his media conference ahead of their FA Cup fourth-round clash against West Ham United at Anfield on Saturday, Klopp delivered an update on Liverpool’s transfer dealings.
“As I’ve said, we are always busy, we are always working and we always check the possibilities,” Klopp said.
“That’s what we’ve done since I’ve been here. Now it’s close to the closing of the window, so if something happens, we will see.
“But there is nothing to say at this moment. If we were to be close to something, everything I could say now would disturb this – and if not, it’s the same situation, so we have nothing to say.
“You’ll have to wait, like I have to wait maybe. I have no problem with this, it is like it is. I am fine with the squad. Everybody can see the squad was never a problem, not for one second, it’s all about injuries and the number of games – that doesn’t fit too good.
“That’s the reason why we’ve thought about a few things but only if it makes real sense for us.”
Klopp has already signed Serbian teenager Marko Grujic from Red Star Belgrade and Queens Park Rangers defender Steven Caulker on loan in the January transfer window.
The Reds booked their place in the League Cup final on Tuesday night thanks to a 6-5 penalty shootout victory over Stoke City at Anfield.
Liverpool have already lost twice to West Ham in the Premier League this season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news